Pub Date : 2024-11-16DOI: 10.1016/j.chaos.2024.115734
Shangling He , Xi Peng , Yingji He , Chun Shan , Dongmei Deng
We present the propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam (CCPGVB) in the Fractional nonlinear Schrödinger equation (FNSE) numerically and find some interesting behaviors. The CCPGVB can propagate like quasi solitons along the propagation direction. The autofocusing effect of the CCPGVB gets stronger while the autofocusing length monotonously decreases and the number of focus become lessen as the Lévy index approaches 2. By adjusting the Lévy index, the chirp factor , the input power , as well as the order of the off-axis vortex pair , the results show that these factors can effectively control the propagation dynamics of the CCPGVB, including intensity distribution, focal length, focal intensity, the light spot and the number of focus. Finally, the Poynting vector and the angular momentum of the CCPGVB prove the autofocusing and diffraction behaviors.
{"title":"Propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam in the fractional nonlinear Schrödinger equation","authors":"Shangling He , Xi Peng , Yingji He , Chun Shan , Dongmei Deng","doi":"10.1016/j.chaos.2024.115734","DOIUrl":"10.1016/j.chaos.2024.115734","url":null,"abstract":"<div><div>We present the propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam (CCPGVB) in the Fractional nonlinear Schrödinger equation (FNSE) numerically and find some interesting behaviors. The CCPGVB can propagate like quasi solitons along the propagation direction. The autofocusing effect of the CCPGVB gets stronger while the autofocusing length monotonously decreases and the number of focus become lessen as the Lévy index approaches 2. By adjusting the Lévy index, the chirp factor <span><math><mi>β</mi></math></span>, the input power <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi><mi>n</mi></mrow></msub></math></span>, as well as the order of the off-axis vortex pair <span><math><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>l</mi><mo>)</mo></mrow></math></span>, the results show that these factors can effectively control the propagation dynamics of the CCPGVB, including intensity distribution, focal length, focal intensity, the light spot and the number of focus. Finally, the Poynting vector and the angular momentum of the CCPGVB prove the autofocusing and diffraction behaviors.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115734"},"PeriodicalIF":5.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650738","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 : 2024-11-16DOI: 10.1016/j.chaos.2024.115749
Subhan Ullah , Amir Ali , Ikram Ullah , Mohammad Mahtab Alam , Zareen A. Khan
Nanofluids have gained significant attention for enhancing heat and mass transfer, particularly in complex flow configurations like convergent and divergent channels. Key applications include improved solar collectors, cooling in heat exchangers, nuclear reactors, drug delivery, thermoelectric systems, reduced friction in lubrication and thermal therapies. In this context, the present research examines the impact of Darcy-Forchheimer aspect on Jeffery-Hamel nanofluids flow through non-parallel converging/diverging channels. The behavior of nanoparticles is exhibited and investigated through the Buongiorno model for nanomaterials. Enhancing thermal efficiency is crucial for many fluids, and this study aims to explore its significance. As the increment in thermal efficiency of many fluids can be more important. The influence of Soret Dufour aspects, heat source, and activation energy are also come upon in current study. Lorentz force, solar radiation and thermal radiations are further examine arises due to the magnetic field application. The current main system of differential equations is converted into ordinary differential equations by appropriate transformations. The obtained systems of are numerically simulated with the help of Mathematica-9 software utilizing the NDSolve technique. The consequences of various physical factors on subjective distributions and engineering quantities are examined. In addition, validation of numerical technique also provided.
{"title":"Activation energy and non-Darcy effects on magnetized Jeffery-Hamel (JH) flow in convergent/divergent channels","authors":"Subhan Ullah , Amir Ali , Ikram Ullah , Mohammad Mahtab Alam , Zareen A. Khan","doi":"10.1016/j.chaos.2024.115749","DOIUrl":"10.1016/j.chaos.2024.115749","url":null,"abstract":"<div><div>Nanofluids have gained significant attention for enhancing heat and mass transfer, particularly in complex flow configurations like convergent and divergent channels. Key applications include improved solar collectors, cooling in heat exchangers, nuclear reactors, drug delivery, thermoelectric systems, reduced friction in lubrication and thermal therapies. In this context, the present research examines the impact of Darcy-Forchheimer aspect on Jeffery-Hamel nanofluids flow through non-parallel converging/diverging channels. The behavior of nanoparticles is exhibited and investigated through the Buongiorno model for nanomaterials. Enhancing thermal efficiency is crucial for many fluids, and this study aims to explore its significance. As the increment in thermal efficiency of many fluids can be more important. The influence of Soret Dufour aspects, heat source, and activation energy are also come upon in current study. Lorentz force, solar radiation and thermal radiations are further examine arises due to the magnetic field application. The current main system of differential equations is converted into ordinary differential equations by appropriate transformations. The obtained systems of are numerically simulated with the help of Mathematica-9 software utilizing the NDSolve technique. The consequences of various physical factors on subjective distributions and engineering quantities are examined. In addition, validation of numerical technique also provided.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115749"},"PeriodicalIF":5.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650724","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 : 2024-11-16DOI: 10.1016/j.chaos.2024.115719
Anthony Couthures , Vineeth Satheeskumar Varma , Samson Lasaulce , Irinel - Constantin Morărescu
We consider a set of individuals, referred to as agents, whose opinions evolve according to nonlinear dynamics. Their opinions impact their behavior or actions, which in turn affect their local environment (for example, via pollution, contamination of a virus, etc.). Each agent can also perceive or observe a signal about the environment, and is influenced by this external signal. This yields a coupled dynamics (opinion and external signal), which behaves in a similar manner to the prey–predator models. One of the main features of our study is that the information provided by the external signal has a significant impact on the opinion dynamics. When the coupling is strong, the external signal may induce either chaotic behavior or convergence towards a limit cycle. When the coupling with the external signal is weak, the classical behavior characterized by local agreements in polarized clusters is observed. In both cases, conditions under which clusters of individuals do not change their actions are provided. Numerical examples are provided to illustrate the derived analytical results.
{"title":"Analysis of an opinion dynamics model coupled with an external environmental dynamics","authors":"Anthony Couthures , Vineeth Satheeskumar Varma , Samson Lasaulce , Irinel - Constantin Morărescu","doi":"10.1016/j.chaos.2024.115719","DOIUrl":"10.1016/j.chaos.2024.115719","url":null,"abstract":"<div><div>We consider a set of individuals, referred to as agents, whose opinions evolve according to nonlinear dynamics. Their opinions impact their behavior or actions, which in turn affect their local environment (for example, via pollution, contamination of a virus, etc.). Each agent can also perceive or observe a signal about the environment, and is influenced by this external signal. This yields a coupled dynamics (opinion and external signal), which behaves in a similar manner to the prey–predator models. One of the main features of our study is that the information provided by the external signal has a significant impact on the opinion dynamics. When the coupling is strong, the external signal may induce either chaotic behavior or convergence towards a limit cycle. When the coupling with the external signal is weak, the classical behavior characterized by local agreements in polarized clusters is observed. In both cases, conditions under which clusters of individuals do not change their actions are provided. Numerical examples are provided to illustrate the derived analytical results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115719"},"PeriodicalIF":5.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650725","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 : 2024-11-16DOI: 10.1016/j.chaos.2024.115737
Rami Ahmad El-Nabulsi
Nonlinear partial differential equations admitting traveling wave solutions play an important role in the description and analysis of real-life physical processes and nonlinear phenomena. In this study, we prove that the excitable reaction-diffusion-convection system introduced by Kopell and Howard can exhibit, in fractal dimensions, a large variety of spatial patterns. We have considered two independent models: a local reaction-diffusion-convection model characterized by variable coefficients that are subject to particular power laws and a nonlocal reaction-diffusion model characterized by symmetric kernels and a variable diffusion coefficient. Each model is characterized by a number of motivating properties and features. In the 1st model, the amplitude is governed by a 2nd-order differential equation, whereas in the 2nd-model, the amplitude is governed by a 4th-order differential equation, which is, under some conditions, comparable to the Swift-Hohenberg equation with variable coefficients that arise in the study of pattern formation, which belongs to the family of extended Fisher-Kolmogorov stationary equations used to study pattern-forming systems in biological and chemical systems. We report the emergence of superstructures that are suppressed for fractal dimensions much less than unity. These superstructures include superspiral waves characterized by a circular symmetry detected in various oscillatory media and the emergence of reflection of waves that take place in non-uniform reaction-diffusion systems, besides the emergence of micro-spiral waves that emerge at the cellular level. A transition from spiral waves to perfectly rotating waves is observed, besides a transition from Mexican hat shaped solutions to upside-down Mexican hat shaped solutions. The domain size has a very strong impact on the rotational frequency of spiral and circular waves. These new phenomena associated with configuration patterns through a reaction-diffusion-convection system with different scales and characterized by variable coefficients can be applied for modeling a wide class of reaction-diffusion-convection problems. Supplementary properties have been obtained and discussed accordingly.
{"title":"Transition from circular to spiral waves and from Mexican hat to upside-down Mexican hat-solutions: The cases of local and nonlocal λ−ω reaction-diffusion-convection fractal systems with variable coefficients","authors":"Rami Ahmad El-Nabulsi","doi":"10.1016/j.chaos.2024.115737","DOIUrl":"10.1016/j.chaos.2024.115737","url":null,"abstract":"<div><div>Nonlinear partial differential equations admitting traveling wave solutions play an important role in the description and analysis of real-life physical processes and nonlinear phenomena. In this study, we prove that the excitable <span><math><mi>λ</mi><mo>−</mo><mi>ω</mi></math></span>reaction-diffusion-convection system introduced by Kopell and Howard can exhibit, in fractal dimensions, a large variety of spatial patterns. We have considered two independent models: a local reaction-diffusion-convection model characterized by variable coefficients that are subject to particular power laws and a nonlocal reaction-diffusion model characterized by symmetric kernels and a variable diffusion coefficient. Each model is characterized by a number of motivating properties and features. In the 1st model, the amplitude is governed by a 2nd-order differential equation, whereas in the 2nd-model, the amplitude is governed by a 4th-order differential equation, which is, under some conditions, comparable to the Swift-Hohenberg equation with variable coefficients that arise in the study of pattern formation, which belongs to the family of extended Fisher-Kolmogorov stationary equations used to study pattern-forming systems in biological and chemical systems. We report the emergence of superstructures that are suppressed for fractal dimensions much less than unity. These superstructures include superspiral waves characterized by a circular symmetry detected in various oscillatory media and the emergence of reflection of waves that take place in non-uniform reaction-diffusion systems, besides the emergence of micro-spiral waves that emerge at the cellular level. A transition from spiral waves to perfectly rotating waves is observed, besides a transition from Mexican hat shaped solutions to upside-down Mexican hat shaped solutions. The domain size has a very strong impact on the rotational frequency of spiral and circular waves. These new phenomena associated with configuration patterns through a reaction-diffusion-convection system with different scales and characterized by variable coefficients can be applied for modeling a wide class of reaction-diffusion-convection problems. Supplementary properties have been obtained and discussed accordingly.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115737"},"PeriodicalIF":5.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650720","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 : 2024-11-16DOI: 10.1016/j.chaos.2024.115741
Rui-Yang Cai , Hua-Cheng Zhou
This paper focuses on the boundary control matched disturbance rejection problem for Caputo-Hadamard fractional heat equations with time delay. By utilizing the novel idea of the active disturbance rejection control (ADRC) approach, two infinite-dimensional systems are constructed. One separates the disturbance from the control input, and the other estimates the unknown disturbance without high gain. By employing the backstepping method, together with the disturbance-compensator, a desired stabilizing controller is designed, and the asymptotical stability is achieved for the original system.
{"title":"Boundary disturbance rejection for Caputo-Hadamard fractional heat equations via ADRC approach","authors":"Rui-Yang Cai , Hua-Cheng Zhou","doi":"10.1016/j.chaos.2024.115741","DOIUrl":"10.1016/j.chaos.2024.115741","url":null,"abstract":"<div><div>This paper focuses on the boundary control matched disturbance rejection problem for Caputo-Hadamard fractional heat equations with time delay. By utilizing the novel idea of the active disturbance rejection control (ADRC) approach, two infinite-dimensional systems are constructed. One separates the disturbance from the control input, and the other estimates the unknown disturbance without high gain. By employing the backstepping method, together with the disturbance-compensator, a desired stabilizing controller is designed, and the asymptotical stability is achieved for the original system.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115741"},"PeriodicalIF":5.3,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650726","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 : 2024-11-15DOI: 10.1016/j.chaos.2024.115721
Yansu Ji, Xiaochen Mao
This paper studies the dynamics of a thermosensitive neuronal network with delayed chemical synapses under electromagnetic induction. The stability and different bifurcations of the network are analyzed. Abundant and interesting bursting oscillations are explored, such as point–point bursting, cycle–cycle bursting, point-cycle bursting and cycle-point bursting oscillations. Time delay plays important roles in the system dynamics, including the amplitude of the spiking state and the delay interval of the subcritical Hopf bifurcation. The average Hamiltonian energy is considered to estimate the synchronized behaviors between neurons, such as intermittent synchronization. As the strength of the chemical synapses varies, asynchronous behaviors, intermittently synchronized and fully synchronized states are observed. The influences of the feedback strength gain of external stimuli induced by electromagnetic induction and temperature coefficient on the synchronized dynamics are discussed. Based on the exponential function circuit, time delay circuit and transfer function circuit, the circuit platform of the network is constructed. The responses of the circuit reach an agreement with the obtained results.
{"title":"Fast and slow dynamical behaviors of delayed-coupled thermosensitive neurons under electromagnetic induction","authors":"Yansu Ji, Xiaochen Mao","doi":"10.1016/j.chaos.2024.115721","DOIUrl":"10.1016/j.chaos.2024.115721","url":null,"abstract":"<div><div>This paper studies the dynamics of a thermosensitive neuronal network with delayed chemical synapses under electromagnetic induction. The stability and different bifurcations of the network are analyzed. Abundant and interesting bursting oscillations are explored, such as point–point bursting, cycle–cycle bursting, point-cycle bursting and cycle-point bursting oscillations. Time delay plays important roles in the system dynamics, including the amplitude of the spiking state and the delay interval of the subcritical Hopf bifurcation. The average Hamiltonian energy is considered to estimate the synchronized behaviors between neurons, such as intermittent synchronization. As the strength of the chemical synapses varies, asynchronous behaviors, intermittently synchronized and fully synchronized states are observed. The influences of the feedback strength gain of external stimuli induced by electromagnetic induction and temperature coefficient on the synchronized dynamics are discussed. Based on the exponential function circuit, time delay circuit and transfer function circuit, the circuit platform of the network is constructed. The responses of the circuit reach an agreement with the obtained results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115721"},"PeriodicalIF":5.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650736","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 : 2024-11-15DOI: 10.1016/j.chaos.2024.115723
Fan Shi , Yinghong Cao , Santo Banerjee , Adil M. Ahmad , Jun Mou
With the increased understanding of information transfer and interactions between neurons, there is an urgent need for a memory element with bionic properties to probe the activity between neurons. Based on this, this paper constructs a novel Memristor Coupled Memcapacitor Synapse Hopfield Neural (MCMSHN) network by creating an element with a memristor coupled memcapacitor and applying it to a Hopfield neural network to simulate synaptic function. Firstly, the memory properties possessed by the Memristor Coupled Memcapacitor Synapse (MCMS) are demonstrated. Secondly, the complex dynamic behavior of MCMSHN is explored by means of numerical simulations to demonstrate its bionic properties. And the study focuses on the dynamical behavior of the synaptic weights and the coupling strengths, including multiple bifurcation behaviors, bionic discharges, and extreme multistability features of the MCMSHN. Finally, the attractors generated by the system are realized by Digital Signal Processing (DSP) techniques. The feasibility of MCMS for estimating synaptic activity is verified from multiple perspectives, providing insights into the complex working mechanisms of the brain.
{"title":"A novel neural networks with memristor coupled memcapacitor-synapse neuron","authors":"Fan Shi , Yinghong Cao , Santo Banerjee , Adil M. Ahmad , Jun Mou","doi":"10.1016/j.chaos.2024.115723","DOIUrl":"10.1016/j.chaos.2024.115723","url":null,"abstract":"<div><div>With the increased understanding of information transfer and interactions between neurons, there is an urgent need for a memory element with bionic properties to probe the activity between neurons. Based on this, this paper constructs a novel Memristor Coupled Memcapacitor Synapse Hopfield Neural (MCMSHN) network by creating an element with a memristor coupled memcapacitor and applying it to a Hopfield neural network to simulate synaptic function. Firstly, the memory properties possessed by the Memristor Coupled Memcapacitor Synapse (MCMS) are demonstrated. Secondly, the complex dynamic behavior of MCMSHN is explored by means of numerical simulations to demonstrate its bionic properties. And the study focuses on the dynamical behavior of the synaptic weights and the coupling strengths, including multiple bifurcation behaviors, bionic discharges, and extreme multistability features of the MCMSHN. Finally, the attractors generated by the system are realized by Digital Signal Processing (DSP) techniques. The feasibility of MCMS for estimating synaptic activity is verified from multiple perspectives, providing insights into the complex working mechanisms of the brain.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115723"},"PeriodicalIF":5.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650735","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 : 2024-11-15DOI: 10.1016/j.chaos.2024.115710
Yupeng Shen, Yaan Li, Weijia Li, Quanmao Yao
Phase space reconstruction plays an indispensable role in nonlinear engineering applications, and the quality of the reconstructed attractor depends on the optimal estimation of delay time and embedding dimension. This study mainly proposes a novel solution strategy for optimal delay time, which can lead to statistically equivalent reconstructions. First, a novel generalized fined-grained multiscale information entropy with multi-feature extraction (GFMIEME) is proposed, which exhibits excellent separability for various noises and chaotic signals. GFMIEME can preserve more original information and features of the target signals while ensuring processing efficiency. The design of multi-feature extraction helps to solve the problem that the mutation features are smoothed in multi-scale analysis, such as the violent fluctuations of signal amplitude and frequency are weakened. Then, based on GFMIEME, an improved mutual information method is developed to estimate delay time precisely. This method ensures the optimal estimation of the delay time for target signals through multiscale and multi-feature analysis. Final, phase space reconstruction is performed on the chaotic signals generated by the Lorenz and Liu systems to evaluate the effectiveness of the GFMIEME-based mutual information method to estimate the optimal delay time. Moreover, the robustness of the proposed method to noise under different signal-to-noise ratios (SNRs) is analyzed. The simulation results illustrate that the improved mutual information method can extract multiscale and multi-feature information from chaotic signals, and estimate the optimal delay time. The reconstructed attractors have a topological structure similar to the original system. Compared with the traditional delay time estimation methods, the proposed GFMIEME-based mutual information method exhibits better robustness to noise. When the SNR reaches -25 dB, the optimal delay times of the Lorenz and Liu attractors can still be estimated successfully.
相空间重构在非线性工程应用中发挥着不可或缺的作用，而重构吸引子的质量取决于延迟时间和嵌入维度的最优估计。本研究主要针对延迟时间的最优化提出了一种新的求解策略，该策略可实现统计等效的重构。首先，提出了一种新颖的广义细粒度多尺度信息熵与多特征提取（GFMIEME），它对各种噪声和混沌信号都表现出极佳的分离性。GFMIEME 可以保留目标信号更多的原始信息和特征，同时确保处理效率。多特征提取的设计有助于解决多尺度分析中突变特征被平滑化的问题，如信号振幅和频率的剧烈波动被弱化。然后，在 GFMIEME 的基础上，开发了一种改进的互信息方法来精确估计延迟时间。该方法通过多尺度和多特征分析，确保目标信号延迟时间的最优估计。最后，对 Lorenz 和 Liu 系统产生的混沌信号进行了相空间重构，以评估基于 GFMIEME 的互信息方法估计最佳延迟时间的有效性。此外，还分析了所提方法在不同信噪比（SNR）下对噪声的鲁棒性。仿真结果表明，改进的互信息方法可以从混沌信号中提取多尺度和多特征信息，并估计出最佳延迟时间。重建的吸引子具有与原始系统相似的拓扑结构。与传统的延迟时间估计方法相比，基于 GFMIEME 的互信息方法对噪声具有更好的鲁棒性。当信噪比达到 -25 dB 时，仍能成功估计出 Lorenz 和 Liu 吸引子的最佳延迟时间。
{"title":"Generalized fined-grained multiscale information entropy with multi-feature extraction and its application in phase space reconstruction","authors":"Yupeng Shen, Yaan Li, Weijia Li, Quanmao Yao","doi":"10.1016/j.chaos.2024.115710","DOIUrl":"10.1016/j.chaos.2024.115710","url":null,"abstract":"<div><div>Phase space reconstruction plays an indispensable role in nonlinear engineering applications, and the quality of the reconstructed attractor depends on the optimal estimation of delay time and embedding dimension. This study mainly proposes a novel solution strategy for optimal delay time, which can lead to statistically equivalent reconstructions. First, a novel generalized fined-grained multiscale information entropy with multi-feature extraction (GFMIEME) is proposed, which exhibits excellent separability for various noises and chaotic signals. GFMIEME can preserve more original information and features of the target signals while ensuring processing efficiency. The design of multi-feature extraction helps to solve the problem that the mutation features are smoothed in multi-scale analysis, such as the violent fluctuations of signal amplitude and frequency are weakened. Then, based on GFMIEME, an improved mutual information method is developed to estimate delay time precisely. This method ensures the optimal estimation of the delay time for target signals through multiscale and multi-feature analysis. Final, phase space reconstruction is performed on the chaotic signals generated by the Lorenz and Liu systems to evaluate the effectiveness of the GFMIEME-based mutual information method to estimate the optimal delay time. Moreover, the robustness of the proposed method to noise under different signal-to-noise ratios (SNRs) is analyzed. The simulation results illustrate that the improved mutual information method can extract multiscale and multi-feature information from chaotic signals, and estimate the optimal delay time. The reconstructed attractors have a topological structure similar to the original system. Compared with the traditional delay time estimation methods, the proposed GFMIEME-based mutual information method exhibits better robustness to noise. When the SNR reaches -25 dB, the optimal delay times of the Lorenz and Liu attractors can still be estimated successfully.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115710"},"PeriodicalIF":5.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650840","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 : 2024-11-15DOI: 10.1016/j.chaos.2024.115733
Hasan Akın
In this paper, we introduce an Ising model with mixed spin (abbreviated as -MSIM) for any spin set on a semi-infinite second-order Cayley tree and construct translation-invariant splitting Gibbs measures (TISGMs) associated with the model. We prove that as the weight of the -spin value increases, the repelling region of the fixed point , corresponding to the TISGM, expands, leading to a broadening of the phase transition region. We also study tree-indexed Markov chains associated with the -MSIM. Additionally, we clarify the extremality of the associated disordered phases by utilizing the method of Martinelli, Sinclair, and Weitz (Martinelli et al., 2007). By examining the non-extremality of the disordered phases related to the -MSIM on the Cayley tree using the Kesten–Stigum condition, we extend previous research findings to encompass any set of spins in . Furthermore, we prove that as the weight of the -spin value increases, the region where the disordered phase corresponding to the -MSIM is extreme narrows, while the region where it is non-extreme widens.
{"title":"New disordered phases of the (s,1/2)-mixed spin Ising model for arbitrary spin s","authors":"Hasan Akın","doi":"10.1016/j.chaos.2024.115733","DOIUrl":"10.1016/j.chaos.2024.115733","url":null,"abstract":"<div><div>In this paper, we introduce an Ising model with mixed spin <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></math></span> (abbreviated as <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></math></span>-MSIM) for any spin set <span><math><mrow><mrow><mo>[</mo><mo>−</mo><mi>s</mi><mo>,</mo><mi>s</mi><mo>]</mo></mrow><mo>∩</mo><mi>Z</mi></mrow></math></span> on a semi-infinite second-order Cayley tree and construct translation-invariant splitting Gibbs measures (TISGMs) associated with the model. We prove that as the weight of the <span><math><mi>s</mi></math></span>-spin value increases, the repelling region of the fixed point <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow><mrow><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></msubsup></math></span>, corresponding to the TISGM, expands, leading to a broadening of the phase transition region. We also study tree-indexed Markov chains associated with the <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></math></span>-MSIM. Additionally, we clarify the extremality of the associated disordered phases by utilizing the method of Martinelli, Sinclair, and Weitz (Martinelli et al., 2007). By examining the non-extremality of the disordered phases related to the <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></math></span>-MSIM on the Cayley tree using the Kesten–Stigum condition, we extend previous research findings to encompass any set of spins in <span><math><mrow><mrow><mo>[</mo><mo>−</mo><mi>s</mi><mo>,</mo><mi>s</mi><mo>]</mo></mrow><mo>∩</mo><mi>Z</mi></mrow></math></span>. Furthermore, we prove that as the weight of the <span><math><mi>s</mi></math></span>-spin value increases, the region where the disordered phase corresponding to the <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></math></span>-MSIM is extreme narrows, while the region where it is non-extreme widens.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115733"},"PeriodicalIF":5.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650737","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}
We hereby develop the theory of Turing instability for reaction–diffusion systems defined on -directed hypergraphs, the latter being a generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the head nodes and the tail nodes. This framework encodes thus for a privileged direction for the reaction to occur: the joint action of tail nodes is a driver for the reaction involving head nodes. It thus results a natural generalization of directed networks. Based on a linear stability analysis, we have shown the existence of two Laplace matrices, allowing to analytically prove that Turing patterns, stationary or wave-like, emerge for a much broader set of parameters in the -directed setting. In particular, directionality promotes Turing instability, otherwise absent in the symmetric case. Analytical results are compared to simulations performed by using the Brusselator model defined on a -directed -hyperring, as well as on a -directed random hypergraph.
后者是超图的一种概括，在超图中，形成超门的节点可以共享为两个不相交的集合，即头部节点和尾部节点。因此，这一框架为反应的发生提供了优先方向：尾部节点的联合行动是涉及头部节点的反应的驱动力。因此，它是对有向网络的自然概括。基于线性稳定性分析，我们证明了两个拉普拉斯矩阵的存在，从而可以分析证明图灵模式（静态或波浪状）会在 m 定向设置中出现在更广泛的参数集合中。特别是，方向性会促进图灵不稳定性，而对称情况下则不存在这种现象。分析结果与在 m 向 d 超环以及 m 向随机超图上使用布鲁塞尔器模型进行的模拟结果进行了比较。
{"title":"Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures","authors":"Marie Dorchain , Wilfried Segnou , Riccardo Muolo , Timoteo Carletti","doi":"10.1016/j.chaos.2024.115730","DOIUrl":"10.1016/j.chaos.2024.115730","url":null,"abstract":"<div><div>We hereby develop the theory of Turing instability for reaction–diffusion systems defined on <span><math><mi>m</mi></math></span>-directed hypergraphs, the latter being a generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the head nodes and the tail nodes. This framework encodes thus for a privileged direction for the reaction to occur: the joint action of tail nodes is a driver for the reaction involving head nodes. It thus results a natural generalization of directed networks. Based on a linear stability analysis, we have shown the existence of two Laplace matrices, allowing to analytically prove that Turing patterns, stationary or wave-like, emerge for a much broader set of parameters in the <span><math><mi>m</mi></math></span>-directed setting. In particular, directionality promotes Turing instability, otherwise absent in the symmetric case. Analytical results are compared to simulations performed by using the Brusselator model defined on a <span><math><mi>m</mi></math></span>-directed <span><math><mi>d</mi></math></span>-hyperring, as well as on a <span><math><mi>m</mi></math></span>-directed random hypergraph.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115730"},"PeriodicalIF":5.3,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650839","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号