Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115913
Taichi Yamamoto, Hiroya Nakao, Ryota Kobayashi
Rhythmic activity commonly observed in biological systems, occurring from the cellular level to the organismic level, is typically modeled as limit cycle oscillators. Phase reduction theory serves as a useful analytical framework for elucidating the synchronization mechanism of these oscillators. Essentially, this theory describes the dynamics of a multi-dimensional nonlinear oscillator using a single variable called asymptotic phase. In order to understand and control the rhythmic phenomena in the real world, it is crucial to estimate the asymptotic phase from the observed data. In this study, we propose a new method, Gaussian Process Phase Interpolation (GPPI), for estimating the asymptotic phase from time series data. The GPPI method first evaluates the asymptotic phase on the limit cycle and subsequently estimates the asymptotic phase outside the limit cycle employing Gaussian process regression. Thanks to the high expressive power of Gaussian processes, the GPPI is capable of capturing a variety of functions. Furthermore, it is easily applicable even when the dimension of the system increases. The performance of the GPPI is tested by using simulation data from the Stuart-Landau oscillator and the Hodgkin–Huxley oscillator. The results demonstrate that the GPPI can accurately estimate the asymptotic phase even in the presence of high observation noise and strong nonlinearity. Additionally, the GPPI is demonstrated as an effective tool for data-driven phase control of a Hodgkin–Huxley oscillator. Thus, the proposed GPPI will facilitate the data-driven modeling of the limit cycle oscillators.
{"title":"Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data","authors":"Taichi Yamamoto, Hiroya Nakao, Ryota Kobayashi","doi":"10.1016/j.chaos.2024.115913","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115913","url":null,"abstract":"Rhythmic activity commonly observed in biological systems, occurring from the cellular level to the organismic level, is typically modeled as limit cycle oscillators. Phase reduction theory serves as a useful analytical framework for elucidating the synchronization mechanism of these oscillators. Essentially, this theory describes the dynamics of a multi-dimensional nonlinear oscillator using a single variable called asymptotic phase. In order to understand and control the rhythmic phenomena in the real world, it is crucial to estimate the asymptotic phase from the observed data. In this study, we propose a new method, Gaussian Process Phase Interpolation (GPPI), for estimating the asymptotic phase from time series data. The GPPI method first evaluates the asymptotic phase on the limit cycle and subsequently estimates the asymptotic phase outside the limit cycle employing Gaussian process regression. Thanks to the high expressive power of Gaussian processes, the GPPI is capable of capturing a variety of functions. Furthermore, it is easily applicable even when the dimension of the system increases. The performance of the GPPI is tested by using simulation data from the Stuart-Landau oscillator and the Hodgkin–Huxley oscillator. The results demonstrate that the GPPI can accurately estimate the asymptotic phase even in the presence of high observation noise and strong nonlinearity. Additionally, the GPPI is demonstrated as an effective tool for data-driven phase control of a Hodgkin–Huxley oscillator. Thus, the proposed GPPI will facilitate the data-driven modeling of the limit cycle oscillators.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"71 31 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115940
Farideh Motaghian, Soheila Nazari, Reza Jafari, Juan P. Dominguez-Morales
Different neurons in biological brain systems can self-organize to create distinct neural circuits that enable a range of cognitive activities. Spiking neural networks (SNNs), which have higher biological and processing capacity than traditional neural networks, are one field of investigation for brain-like computing. A neural computational model with a recurrent network structure based on SNN is a liquid state machine (LSM). This research proposes a novel LSM structure, where the output layer comprises classification pyramid neurons, the intermediate layer is the liquid layer, and the input layer is generated from the retina model. In this research, the liquid layer is considered a modular complex network. The number of clusters in the liquid layer corresponds to the number of hidden patterns in the data, thus increasing the classification accuracy in the data. As this network is sparse, the computational time can be reduced, and the network learns faster than a fully connected network. Using this concept, we can expand the interior of the liquid layer in the LSM into some clusters rather than taking random connections into account as in other studies. Subsequently, an unsupervised Power-Spike Time Dependent Plasticity (Pow-STDP) learning technique is considered to optimize the synaptic connections between the liquid and output layers. The performance of the suggested LSM structure was very impressive compared to deep and spiking classification networks using three challenging datasets: MNIST, CIFAR-10, and CIFAR-100. Accuracy improvements over previous spiking networks were demonstrated by the accuracy of 98.1 % (6 training epochs), 95.4 % (6 training epochs), and 75.52 % (20 training epochs) that were obtained, respectively. The suggested network not only demonstrates more accuracy when compared to earlier spike-based learning techniques, but it also has a faster rate of convergence during the training phase. The benefits of the suggested network include unsupervised learning, minimal power consumption if used on neuromorphic devices, higher classification accuracy, and lower training epochs (higher training speed).
{"title":"Application of modular and sparse complex networks in enhancing connectivity patterns of liquid state machines","authors":"Farideh Motaghian, Soheila Nazari, Reza Jafari, Juan P. Dominguez-Morales","doi":"10.1016/j.chaos.2024.115940","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115940","url":null,"abstract":"Different neurons in biological brain systems can self-organize to create distinct neural circuits that enable a range of cognitive activities. Spiking neural networks (SNNs), which have higher biological and processing capacity than traditional neural networks, are one field of investigation for brain-like computing. A neural computational model with a recurrent network structure based on SNN is a liquid state machine (LSM). This research proposes a novel LSM structure, where the output layer comprises classification pyramid neurons, the intermediate layer is the liquid layer, and the input layer is generated from the retina model. In this research, the liquid layer is considered a modular complex network. The number of clusters in the liquid layer corresponds to the number of hidden patterns in the data, thus increasing the classification accuracy in the data. As this network is sparse, the computational time can be reduced, and the network learns faster than a fully connected network. Using this concept, we can expand the interior of the liquid layer in the LSM into some clusters rather than taking random connections into account as in other studies. Subsequently, an unsupervised Power-Spike Time Dependent Plasticity (Pow-STDP) learning technique is considered to optimize the synaptic connections between the liquid and output layers. The performance of the suggested LSM structure was very impressive compared to deep and spiking classification networks using three challenging datasets: MNIST, CIFAR-10, and CIFAR-100. Accuracy improvements over previous spiking networks were demonstrated by the accuracy of 98.1 % (6 training epochs), 95.4 % (6 training epochs), and 75.52 % (20 training epochs) that were obtained, respectively. The suggested network not only demonstrates more accuracy when compared to earlier spike-based learning techniques, but it also has a faster rate of convergence during the training phase. The benefits of the suggested network include unsupervised learning, minimal power consumption if used on neuromorphic devices, higher classification accuracy, and lower training epochs (higher training speed).","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"32 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115890
Xiaohui Wang, Xianlong Fu
This paper considers the existence and stability of pth Weyl almost automorphic solutions in distribution for a class of neutral stochastic functional differential equations. It is first proved by Banach fixed point theorem that the equation has a unique Lp-bounded and uniformly Lp-continuous solution, and then, this solution is further checked to be pth Weyl almost automorphic in distribution. The global exponential stability and almost sure exponential stability of pth Weyl almost automorphic solutions in distribution are also discussed for the considered equation under some conditions. In the end, an example is given to illustrate the obtained results.
{"title":"Existence and stability of [formula omitted]th Weyl almost automorphic solutions in distribution for neutral stochastic FDEs","authors":"Xiaohui Wang, Xianlong Fu","doi":"10.1016/j.chaos.2024.115890","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115890","url":null,"abstract":"This paper considers the existence and stability of <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>th Weyl almost automorphic solutions in distribution for a class of neutral stochastic functional differential equations. It is first proved by Banach fixed point theorem that the equation has a unique <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-bounded and uniformly <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-continuous solution, and then, this solution is further checked to be <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>th Weyl almost automorphic in distribution. The global exponential stability and almost sure exponential stability of <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>th Weyl almost automorphic solutions in distribution are also discussed for the considered equation under some conditions. In the end, an example is given to illustrate the obtained results.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"305 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115949
Vladislav Soukhovolsky, Anton Kovalev, Olga Tarasova, Viatcheslav Martemyanov
To understand regulatory processes in insects, it is proposed here to evaluate regulatory characteristics of various populations. For this purpose, regulatory characteristics were analyzed for many time series of forest insect abundance dynamics and of area of damage to forest stands by forest insects; these characteristics reflect positive and negative feedback in populations. To describe the density dynamics of insect populations, an autoregressive (AR) model is proposed, according to which current population density is determined by its order k: population density in k preceding years. To estimate order k, partial autocorrelation functions of many time series of insect abundance dynamics were used. AR models were constructed for 33 populations of 15 species of phyllophagous insects. It was found that all the examined populations are described rather accurately (with high determination coefficients Radj2) by second-order AR models. Two characteristics of regulatory processes in a population are introduced in this work: coefficient a1 characterizes a positive relation between current population density and its density in the preceding year, and coefficient a2 reflects negative feedback between population densities in years i - 2 and i. It was demonstrated that for all the studied populations, the regulatory coefficients—regardless of a variance of population densities—vary within a relatively narrow range. To discuss reasons for the narrow range of the characteristics of regulatory processes in diverse populations, it is suggested to use indicators of their stability as an ability of a system to restore an equilibrium state that the system left under the influence of perturbing factors. For the analyzed populations, stability margins of second-order AR models were calculated, as were spectra of abundance dynamics of the time series under study. It was shown that the narrow range of regulatory characteristics for the time series of forest insects' population density can be explained by possible existence of oscillatory modes in populations.
{"title":"Regulatory characteristics of population density dynamics of forest insects and possible reasons for the observed narrow range of such characteristics","authors":"Vladislav Soukhovolsky, Anton Kovalev, Olga Tarasova, Viatcheslav Martemyanov","doi":"10.1016/j.chaos.2024.115949","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115949","url":null,"abstract":"To understand regulatory processes in insects, it is proposed here to evaluate regulatory characteristics of various populations. For this purpose, regulatory characteristics were analyzed for many time series of forest insect abundance dynamics and of area of damage to forest stands by forest insects; these characteristics reflect positive and negative feedback in populations. To describe the density dynamics of insect populations, an autoregressive (AR) model is proposed, according to which current population density is determined by its order <ce:italic>k</ce:italic>: population density in <ce:italic>k</ce:italic> preceding years. To estimate order <ce:italic>k</ce:italic>, partial autocorrelation functions of many time series of insect abundance dynamics were used. AR models were constructed for 33 populations of 15 species of phyllophagous insects. It was found that all the examined populations are described rather accurately (with high determination coefficients R<ce:inf loc=\"post\">adj</ce:inf><ce:sup loc=\"post\">2</ce:sup>) by second-order AR models. Two characteristics of regulatory processes in a population are introduced in this work: coefficient <ce:italic>a</ce:italic><ce:inf loc=\"post\"><ce:italic>1</ce:italic></ce:inf> characterizes a positive relation between current population density and its density in the preceding year, and coefficient <ce:italic>a</ce:italic><ce:inf loc=\"post\"><ce:italic>2</ce:italic></ce:inf> reflects negative feedback between population densities in years <ce:italic>i</ce:italic> - 2 and <ce:italic>i</ce:italic>. It was demonstrated that for all the studied populations, the regulatory coefficients—regardless of a variance of population densities—vary within a relatively narrow range. To discuss reasons for the narrow range of the characteristics of regulatory processes in diverse populations, it is suggested to use indicators of their stability as an ability of a system to restore an equilibrium state that the system left under the influence of perturbing factors. For the analyzed populations, stability margins of second-order AR models were calculated, as were spectra of abundance dynamics of the time series under study. It was shown that the narrow range of regulatory characteristics for the time series of forest insects' population density can be explained by possible existence of oscillatory modes in populations.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"32 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115933
Yizhou Yang, Haihong Li, Shun Gao, Qionglin Dai, Junzhong Yang
Opinion dynamics and evolutionary games are two pivotal fields in social dynamics, and the intricate interplay between them has great practical significance and becomes worthy of further exploration. In this work, we investigate the interdependent evolutionary dynamics of opinion and strategy on two-layer networks. On one layer, individuals exchange their viewpoints and update opinions. On the other layer, they play public goods games, and their decisions of whether to invest and how much to invest evolve over time. Based on different time scales as well as different interplay modes of the two dynamics, we consider three schemes, constant-opinion scheme, opinion-guided scheme and mutual-influence scheme. Our results show that the mutual-influence scheme, which incorporates both opinion attraction and opinion repulsion in opinion updating, facilitates the evolution of cooperation best among the three. By observing the distributions and the snapshots of opinions and strategies, we reveal that the heterogeneity in investment and the considerable amount of investment are two key factors contributed to the improvement of cooperation. These results illustrate the critical role that the interplay between opinion dynamics and strategic decision-making plays in addressing the real-world issues concerning collective behavior and resource allocation. Additionally, different convergence and divergence rates for opinion attraction and opinion repulsion in the mutual-influence scheme are considered. This study demonstrates that interdependent evolutionary dynamics of opinion and strategy can be employed to elucidate the intrinsic mechanisms of cooperation evolution and opinion formation.
{"title":"Interdependent evolutionary dynamics of opinion and strategy on two-layer networks","authors":"Yizhou Yang, Haihong Li, Shun Gao, Qionglin Dai, Junzhong Yang","doi":"10.1016/j.chaos.2024.115933","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115933","url":null,"abstract":"Opinion dynamics and evolutionary games are two pivotal fields in social dynamics, and the intricate interplay between them has great practical significance and becomes worthy of further exploration. In this work, we investigate the interdependent evolutionary dynamics of opinion and strategy on two-layer networks. On one layer, individuals exchange their viewpoints and update opinions. On the other layer, they play public goods games, and their decisions of whether to invest and how much to invest evolve over time. Based on different time scales as well as different interplay modes of the two dynamics, we consider three schemes, constant-opinion scheme, opinion-guided scheme and mutual-influence scheme. Our results show that the mutual-influence scheme, which incorporates both opinion attraction and opinion repulsion in opinion updating, facilitates the evolution of cooperation best among the three. By observing the distributions and the snapshots of opinions and strategies, we reveal that the heterogeneity in investment and the considerable amount of investment are two key factors contributed to the improvement of cooperation. These results illustrate the critical role that the interplay between opinion dynamics and strategic decision-making plays in addressing the real-world issues concerning collective behavior and resource allocation. Additionally, different convergence and divergence rates for opinion attraction and opinion repulsion in the mutual-influence scheme are considered. This study demonstrates that interdependent evolutionary dynamics of opinion and strategy can be employed to elucidate the intrinsic mechanisms of cooperation evolution and opinion formation.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"2 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1016/j.chaos.2024.115947
Roshana Mukhtar, Chuan-Yu Chang, Muhammad Asif Zahoor Raja, Naveed Ishtiaq Chaudhary, Muhammad Junaid Ali Asif Raja, Chi-Min Shu
In this study, a novel application of intelligent machine predictive exogenous neuro-structure optimized with the Levenberg-Marquardt (IMPENS-LM) algorithm is presented to analyze the dynamics of fractional innate immune response to nonlinear Parkinson's disease propagation considering the impact of therapeutic interventions (PDP-TI). A novel design of the fractional PDP-TI model is constructed with a nonlinear system of five differential compartments representing healthy neurons and infected neurons, extracellular α-syn, and both active and resting microglia. The presented IMPENS is formulated with neuro-structure of nonlinear autoregressive exogenous neural networks with efficient backpropagation of LM algorithm to solve the scenarios of nonlinear fractional PDP-TI model by varying neuron infection rate, survival percentage of α-syn from the death of infected neurons, the density of microglia, infected neurons death rate due to α-syn aggregations, and the ratio of therapeutic approach targeting α-syn with fixed values of annihilation rate of activated microglia, apoptosis rate of neurons and microglia etc. The IMPENS-LM algorithm is operated on synthetic datasets of fractional PDP-TI system generated through the Grunwald-Letnikov fractional finite difference-based numerical computing paradigm for each variant. The sufficient large numerical experimentation is performed with the IMPENS-LM technique to analyze the behavior of the dynamics of the PDP-TI model with the help of different proximity, complexity, and statistical measures in terms of MSE-based iterative fitness learning arcs, absolute error analysis, error autocorrelation plots, and error histograms, to substantiate the efficacy of stochastic solver on sundry fractional orders.
{"title":"Design of fractional innate immune response to nonlinear Parkinson's disease model with therapeutic intervention: Intelligent machine predictive exogenous networks","authors":"Roshana Mukhtar, Chuan-Yu Chang, Muhammad Asif Zahoor Raja, Naveed Ishtiaq Chaudhary, Muhammad Junaid Ali Asif Raja, Chi-Min Shu","doi":"10.1016/j.chaos.2024.115947","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115947","url":null,"abstract":"In this study, a novel application of intelligent machine predictive exogenous neuro-structure optimized with the Levenberg-Marquardt (IMPENS-LM) algorithm is presented to analyze the dynamics of fractional innate immune response to nonlinear Parkinson's disease propagation considering the impact of therapeutic interventions (PDP-TI). A novel design of the fractional PDP-TI model is constructed with a nonlinear system of five differential compartments representing healthy neurons and infected neurons, extracellular α-syn, and both active and resting microglia. The presented IMPENS is formulated with neuro-structure of nonlinear autoregressive exogenous neural networks with efficient backpropagation of LM algorithm to solve the scenarios of nonlinear fractional PDP-TI model by varying neuron infection rate, survival percentage of <ce:italic>α</ce:italic>-syn from the death of infected neurons, the density of microglia, infected neurons death rate due to <ce:italic>α</ce:italic>-syn aggregations, and the ratio of therapeutic approach targeting <ce:italic>α</ce:italic>-syn with fixed values of annihilation rate of activated microglia, apoptosis rate of neurons and microglia etc. The IMPENS-LM algorithm is operated on synthetic datasets of fractional PDP-TI system generated through the Grunwald-Letnikov fractional finite difference-based numerical computing paradigm for each variant. The sufficient large numerical experimentation is performed with the IMPENS-LM technique to analyze the behavior of the dynamics of the PDP-TI model with the help of different proximity, complexity, and statistical measures in terms of MSE-based iterative fitness learning arcs, absolute error analysis, error autocorrelation plots, and error histograms, to substantiate the efficacy of stochastic solver on sundry fractional orders.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"32 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1016/j.chaos.2024.115926
Shaolong Zeng, Yangfan Hu, Shijing Tan, Biao Wang
The universality of critical phenomena and finite-size scaling are effective methods for measuring critical exponents in experiments and inferring the intrinsic interactions within materials. Here, we establish the finite-size scaling form of the Landau–Ginzburg model for fractal time processes and quantitatively calculate the critical exponents at the upper critical dimension. Interestingly, contrary to the traditional conception that critical exponents are independent of dynamic processes and proportional to correlation length, we find that fractal time processes can not only change critical exponents but also yield a scaling form of size dependent on fractional order and spatial dimension. These theoretical results provide a reasonable method to determine and measure the existence of fractal time processes and their associated critical exponents. The simulations of the Landau–Ginzburg model with fractional temporal derivatives and the Ising model with long-range temporal interactions not only reveal critical exponents distinct from those of standard models but also exhibit unique size effects characteristic of fractal time processes. These results validate the emergence of a new universality class and confirm the predictions of the finite-size scaling theory for fractal time processes.
{"title":"Finite-size scaling of Landau–Ginzburg model for fractal time processes","authors":"Shaolong Zeng, Yangfan Hu, Shijing Tan, Biao Wang","doi":"10.1016/j.chaos.2024.115926","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115926","url":null,"abstract":"The universality of critical phenomena and finite-size scaling are effective methods for measuring critical exponents in experiments and inferring the intrinsic interactions within materials. Here, we establish the finite-size scaling form of the Landau–Ginzburg model for fractal time processes and quantitatively calculate the critical exponents at the upper critical dimension. Interestingly, contrary to the traditional conception that critical exponents are independent of dynamic processes and proportional to correlation length, we find that fractal time processes can not only change critical exponents but also yield a scaling form of size dependent on fractional order and spatial dimension. These theoretical results provide a reasonable method to determine and measure the existence of fractal time processes and their associated critical exponents. The simulations of the Landau–Ginzburg model with fractional temporal derivatives and the Ising model with long-range temporal interactions not only reveal critical exponents distinct from those of standard models but also exhibit unique size effects characteristic of fractal time processes. These results validate the emergence of a new universality class and confirm the predictions of the finite-size scaling theory for fractal time processes.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"12 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-23DOI: 10.1016/j.chaos.2024.115931
Mohammad Haidar, Carla Sayegh
In this paper we investigate an asymptotic limit for Green–Naghdi equation in the KdV scale with uneven bottom and considering the influence of two factors, surface tension and Coriolis effect. We establish the KdV equation of the new model by using Whitham technique then we find the analytic solution in case of flat bottom and Hs explicit consistent solution with correctors of order μ2 in case of uneven bottom. As well as, we obtain an Hs consistent solution for the asymptotic Green–Naghdi equation. Finally, we use Python to ensure the theoretical results through numerical simulations that admit to represent and validate the solution.
{"title":"Asymptotic shallow water equations: Modeling and solutions","authors":"Mohammad Haidar, Carla Sayegh","doi":"10.1016/j.chaos.2024.115931","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115931","url":null,"abstract":"In this paper we investigate an asymptotic limit for Green–Naghdi equation in the KdV scale with uneven bottom and considering the influence of two factors, surface tension and Coriolis effect. We establish the KdV equation of the new model by using Whitham technique then we find the analytic solution in case of flat bottom and <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup></mml:math> explicit consistent solution with correctors of order <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">μ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> in case of uneven bottom. As well as, we obtain an <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup></mml:math> consistent solution for the asymptotic Green–Naghdi equation. Finally, we use Python to ensure the theoretical results through numerical simulations that admit to represent and validate the solution.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"25 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-22DOI: 10.1016/j.chaos.2024.115923
S.V. Talalov
In this study, the problem of the energy spectrum of a quantum vortex loop moving in a thin long pipe is solved for the first time. We quantize this dynamic system using a new method, which leads to non-trivial results for circulation Γ and energy values E. It is shown that the spectrum has a quasi-continuous fractal structure. In the final form, we present the spectrum of the vortex loop in the form of a “Regge trajectory” E=E(Γ). The vortex quantization problem is considered outside of two-fluid hydrodynamics and other conventional approaches. We also discuss ways to improve the model, which could allow us to apply the results we have obtained to describe a quantum turbulent flow.
{"title":"On the group-theoretical approach to energy quantization of a perturbed vortex ring: Spectrum calculating in the pipe-type domain","authors":"S.V. Talalov","doi":"10.1016/j.chaos.2024.115923","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115923","url":null,"abstract":"In this study, the problem of the energy spectrum of a quantum vortex loop moving in a thin long pipe is solved for the first time. We quantize this dynamic system using a new method, which leads to non-trivial results for circulation <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi mathvariant=\"normal\">Γ</mml:mi></mml:math> and energy values <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mi>E</mml:mi></mml:math>. It is shown that the spectrum has a quasi-continuous fractal structure. In the final form, we present the spectrum of the vortex loop in the form of a “Regge trajectory” <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mi>E</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant=\"normal\">Γ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. The vortex quantization problem is considered outside of two-fluid hydrodynamics and other conventional approaches. We also discuss ways to improve the model, which could allow us to apply the results we have obtained to describe a quantum turbulent flow.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"54 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-22DOI: 10.1016/j.chaos.2024.115938
Christos N. Veinidis, Marialena Akriotou, Alex Kondi, Efi-Maria Papia, Vassilios Constantoudis, Dimitris Syvridis
Speckle patterns, arising from the interference of coherent wave fronts scattered by disordered materials, serve as the basis for Optical Physical Unclonable Functions (Optical PUF), offering inherent randomness crucial for generating secure cryptographic keys. This paper investigates the universal properties of speckle images through an analysis of their complexity using a multiscale entropy-based methodology. Utilizing an experimental setup simulating Optical PUFs, eight sets of uncorrelated challenges produce speckle patterns meeting contemporary literature specifications. The Pearson’s Cross-Correlation Coefficient and the cross-correlation function are used to assess the similarity between the speckle patterns within each individual set, by calculating these measures for all possible pairs of corresponding patterns. The entropy-based complexity analysis of these patterns is found to be sensitive to their grain size while elucidating in a multiscale fashion the entropy footprint of their short and long-range correlations. Finally, it is shown that the presence of grains in the speckle patterns determines their complexity, while a kind of duality between the challenges and the produced speckle patterns is highlighted.
{"title":"Complexity analysis of challenges and speckle patterns in an Optical Physical Unclonable Function","authors":"Christos N. Veinidis, Marialena Akriotou, Alex Kondi, Efi-Maria Papia, Vassilios Constantoudis, Dimitris Syvridis","doi":"10.1016/j.chaos.2024.115938","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115938","url":null,"abstract":"Speckle patterns, arising from the interference of coherent wave fronts scattered by disordered materials, serve as the basis for Optical Physical Unclonable Functions (Optical PUF), offering inherent randomness crucial for generating secure cryptographic keys. This paper investigates the universal properties of speckle images through an analysis of their complexity using a multiscale entropy-based methodology. Utilizing an experimental setup simulating Optical PUFs, eight sets of uncorrelated challenges produce speckle patterns meeting contemporary literature specifications. The Pearson’s Cross-Correlation Coefficient and the cross-correlation function are used to assess the similarity between the speckle patterns within each individual set, by calculating these measures for all possible pairs of corresponding patterns. The entropy-based complexity analysis of these patterns is found to be sensitive to their grain size while elucidating in a multiscale fashion the entropy footprint of their short and long-range correlations. Finally, it is shown that the presence of grains in the speckle patterns determines their complexity, while a kind of duality between the challenges and the produced speckle patterns is highlighted.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"5 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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