Pub Date : 2025-01-17DOI: 10.1016/j.chaos.2025.116011
Xuetian Zhang, Tianhua Li, Chunrui Zhang
This paper investigates a general two-dimensional discrete model with self-diffusion and cross-diffusion characteristics. We construct the model using the method of coupled map lattices. By conducting bifurcation analysis and Turing instability analysis on the model, we reveal the crucial role of cross-diffusion in the formation of Turing patterns. Through this study, we gain a deeper understanding of the importance of cross-diffusion in discrete dynamics and provide new insights and approaches for research in related fields. As an application, we apply the theory to two practical models and get very meaningful conclusions. For predator–prey model, cross diffusion coefficient determines the level of danger and driving force exerted by the predators on the prey. When the predators pose a lower level of danger and exert a weaker driving force on the prey, the prey population can maintain a spatially homogeneous state. However, when the predators pose a higher level of danger and exert a stronger driving force on the prey, the prey population is likely to exhibit a chaotic and disordered state due to continuous disturbances and fleeing. For tree–grass model, the results reveal indicate that the spatial distribution patterns of tree–grass populations are jointly determined by the frequency of fire occurrences and the effects of cross-diffusion. The former influences the direction of evolution low fire frequency leads to forest evolution, while high fire frequency leads to grassland evolution. The latter affects whether the distribution is uniform; weak cross-diffusion effects allow the tree–grass population to maintain a spatially uniform distribution, while strong cross-diffusion effects are likely to lead to a non-uniform and irregular patchy distribution of the tree–grass population.
{"title":"Pattern formation on coupled map lattices induced by cross-diffusion","authors":"Xuetian Zhang, Tianhua Li, Chunrui Zhang","doi":"10.1016/j.chaos.2025.116011","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116011","url":null,"abstract":"This paper investigates a general two-dimensional discrete model with self-diffusion and cross-diffusion characteristics. We construct the model using the method of coupled map lattices. By conducting bifurcation analysis and Turing instability analysis on the model, we reveal the crucial role of cross-diffusion in the formation of Turing patterns. Through this study, we gain a deeper understanding of the importance of cross-diffusion in discrete dynamics and provide new insights and approaches for research in related fields. As an application, we apply the theory to two practical models and get very meaningful conclusions. For predator–prey model, cross diffusion coefficient determines the level of danger and driving force exerted by the predators on the prey. When the predators pose a lower level of danger and exert a weaker driving force on the prey, the prey population can maintain a spatially homogeneous state. However, when the predators pose a higher level of danger and exert a stronger driving force on the prey, the prey population is likely to exhibit a chaotic and disordered state due to continuous disturbances and fleeing. For tree–grass model, the results reveal indicate that the spatial distribution patterns of tree–grass populations are jointly determined by the frequency of fire occurrences and the effects of cross-diffusion. The former influences the direction of evolution low fire frequency leads to forest evolution, while high fire frequency leads to grassland evolution. The latter affects whether the distribution is uniform; weak cross-diffusion effects allow the tree–grass population to maintain a spatially uniform distribution, while strong cross-diffusion effects are likely to lead to a non-uniform and irregular patchy distribution of the tree–grass population.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"112 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021205","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.116000
Javier Cubillos-Cornejo, Miguel Escobar Mendoza, Ignacio Bordeu
In this work, we explore the influence of coupling strength, network size, and randomness on the collective dynamics of FitzHugh–Nagumo oscillators on complex networks. Using Watts–Strogatz small-world network connectivities, we identify four distinct dynamical phases: chaotic, intermittent, partially synchronized, and fully synchronized. The intermittent phase is characterized by the coexistence of chaotic behavior and chimera states, reminiscent of epileptic-seizure-related (ESR) intermittency observed in the brain. We analyze the inter-spike intervals of the individual oscillators, and the existence, duration, and frequency of ESR events as a function of the system parameters. Furthermore, we study the transitions into and out of the intermittent phase and show that peaks in the probability of extreme events – short transients of anomalously high synchronization – precede the transitions from chaos to intermittency and from partial to full synchronization. These transitions are followed by significant changes in the maximum Lyapunov exponent and Kaplan–Yorke dimension. Finally, we discuss how the coupling strength and network properties can be leveraged to control the system’s state and the potential applications of extreme event analysis in the study of neural data.
{"title":"Extreme events at the onset of epileptic-like intermittent activity of FitzHugh–Nagumo oscillators on small-world networks","authors":"Javier Cubillos-Cornejo, Miguel Escobar Mendoza, Ignacio Bordeu","doi":"10.1016/j.chaos.2025.116000","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116000","url":null,"abstract":"In this work, we explore the influence of coupling strength, network size, and randomness on the collective dynamics of FitzHugh–Nagumo oscillators on complex networks. Using Watts–Strogatz small-world network connectivities, we identify four distinct dynamical phases: chaotic, intermittent, partially synchronized, and fully synchronized. The intermittent phase is characterized by the coexistence of chaotic behavior and chimera states, reminiscent of epileptic-seizure-related (ESR) intermittency observed in the brain. We analyze the inter-spike intervals of the individual oscillators, and the existence, duration, and frequency of ESR events as a function of the system parameters. Furthermore, we study the transitions into and out of the intermittent phase and show that peaks in the probability of extreme events – short transients of anomalously high synchronization – precede the transitions from chaos to intermittency and from partial to full synchronization. These transitions are followed by significant changes in the maximum Lyapunov exponent and Kaplan–Yorke dimension. Finally, we discuss how the coupling strength and network properties can be leveraged to control the system’s state and the potential applications of extreme event analysis in the study of neural data.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"3 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988276","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 : 2025-01-16DOI: 10.1016/j.chaos.2024.115911
Hidekazu Yoshioka
Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as powerful tools in several research fields, including physics, mathematical economics, and environmental engineering. We formulate two novel mathematical models of long memory process based on a superposition of interacting processes driven by jumps. The mutual excitation among the processes to be superposed is assumed to be of the mean field or aggregation form, where the former yields a more analytically tractable model. The statistics of the proposed long memory processes are investigated using their moment-generating function, autocorrelation, and associated generalized Riccati equations. Finally, the proposed models are applied to time series data of migrating fish counts at river observation points. The results of this study suggest that an exponential memory or a long memory model is insufficient; however, a unified method that can cover both is necessary to analyze fish migration, and our model is exactly the case.
{"title":"Superposition of interacting stochastic processes with memory and its application to migrating fish counts","authors":"Hidekazu Yoshioka","doi":"10.1016/j.chaos.2024.115911","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115911","url":null,"abstract":"Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as powerful tools in several research fields, including physics, mathematical economics, and environmental engineering. We formulate two novel mathematical models of long memory process based on a superposition of interacting processes driven by jumps. The mutual excitation among the processes to be superposed is assumed to be of the mean field or aggregation form, where the former yields a more analytically tractable model. The statistics of the proposed long memory processes are investigated using their moment-generating function, autocorrelation, and associated generalized Riccati equations. Finally, the proposed models are applied to time series data of migrating fish counts at river observation points. The results of this study suggest that an exponential memory or a long memory model is insufficient; however, a unified method that can cover both is necessary to analyze fish migration, and our model is exactly the case.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988180","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.116028
Yuqing Xu, Bo Wang, Jing Ye, Jinyun Zhou
In this study, we present a nonreciprocal thermal emitter with dual-polarization capabilities, utilizing a monolayer silicon ring array featuring circular voids. The device demonstrates nonreciprocal behavior under both transverse electric (TE) and transverse magnetic (TM) polarizations, displaying two distinct nonreciprocal peaks in TE polarization and a single peak in TM polarization. Rigorous coupled-wave analysis (RCWA) and validation through coupled-mode theory (CMT) confirm high nonreciprocal efficiency in the mid-infrared region. Specifically, under TE polarization, the two nonreciprocal peaks are observed at wavelengths of 15.074 μm and 15.228 μm, yielding nonreciprocal efficiencies of 94.48 % and 95.65 %, respectively. Under TM polarization, the nonreciprocal peak is positioned at 15.127 μm, with an efficiency of 94.58 %. Allowing for functional differentiation based on the polarization of the incident light. This dual-polarization feature significantly broadens its application potential in thermal management, energy harvesting, and infrared camouflage, particularly enabling more efficient energy conversion and radiation control at small incident angles. Our work offers new insights for future multifunctional nonreciprocal thermal emitters.
{"title":"Thermal non-equilibrium process for nonreciprocity with dual-TE/single-TM peaks","authors":"Yuqing Xu, Bo Wang, Jing Ye, Jinyun Zhou","doi":"10.1016/j.chaos.2025.116028","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116028","url":null,"abstract":"In this study, we present a nonreciprocal thermal emitter with dual-polarization capabilities, utilizing a monolayer silicon ring array featuring circular voids. The device demonstrates nonreciprocal behavior under both transverse electric (TE) and transverse magnetic (TM) polarizations, displaying two distinct nonreciprocal peaks in TE polarization and a single peak in TM polarization. Rigorous coupled-wave analysis (RCWA) and validation through coupled-mode theory (CMT) confirm high nonreciprocal efficiency in the mid-infrared region. Specifically, under TE polarization, the two nonreciprocal peaks are observed at wavelengths of 15.074 μm and 15.228 μm, yielding nonreciprocal efficiencies of 94.48 % and 95.65 %, respectively. Under TM polarization, the nonreciprocal peak is positioned at 15.127 μm, with an efficiency of 94.58 %. Allowing for functional differentiation based on the polarization of the incident light. This dual-polarization feature significantly broadens its application potential in thermal management, energy harvesting, and infrared camouflage, particularly enabling more efficient energy conversion and radiation control at small incident angles. Our work offers new insights for future multifunctional nonreciprocal thermal emitters.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"23 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987821","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.116003
T. Laptyeva, S. Jalan, M. Ivanchenko
Explosive synchronization refers to an abrupt (first order) transition to non-zero value of phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for global higher-order coupling without specific requirements on the individual oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive (de)synchronization transition in multiplex networks, where it is sufficient to have a single random sparsely connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own) and the other layer being a regular lattice without own phase transitions at all. Characteristic timescales in the layers have to be different. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, although the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The explosive transition persists with increasing the system size. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out.
{"title":"Explosive synchronization in multiplex multiple timescale networks with higher-order interactions","authors":"T. Laptyeva, S. Jalan, M. Ivanchenko","doi":"10.1016/j.chaos.2025.116003","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116003","url":null,"abstract":"Explosive synchronization refers to an abrupt (first order) transition to non-zero value of phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for global higher-order coupling without specific requirements on the individual oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive (de)synchronization transition in multiplex networks, where it is sufficient to have a single random sparsely connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own) and the other layer being a regular lattice without own phase transitions at all. Characteristic timescales in the layers have to be different. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, although the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The explosive transition persists with increasing the system size. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"30 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988273","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.116012
Zhouqing Tang, Huihai Wang, Wanting Zhu, Kehui Sun
Memristors play an important role in the modeling of neural networks as external stimuli for neuron excitation and biological synapses for information exchange. Recently, the discrete fracmemristor has shown excellent properties in describing the memory effect of nonlinear systems, including biological nervous systems. In this paper, we propose a fractional memristive Rulkov neuron model (FMRN) by introducing the fractional discrete HP-type memristor (FDM-HP) into a single fractional Rulkov neuron (FRN) as electromagnetic radiation. Their parametric modulation dynamics are investigated and compared by means of firing patterns, Lyapunov exponents, bifurcation diagrams and complexity. In addition, to verify the information transfer ability of discrete fracmemristor as a synaptic model, a fractional bi-neuron system is constructed by coupling two FRNs with FDM-HP, which is further subjected to the analyses of phase synchronization and firing behaviors. The simulation results show that the combination of FDM-HP and FRN can effectively enrich the dynamics of neuron system, achieve synchronous firing rhythms, and generate various novel firing patterns. The researches provide the theoretical and experimental supports for neuronal modeling and synapse-based synchronization, which lay the foundation for further researches on complex neural networks.
{"title":"Dynamics and synchronization of fractional-order Rulkov neuron coupled with discrete fracmemristor","authors":"Zhouqing Tang, Huihai Wang, Wanting Zhu, Kehui Sun","doi":"10.1016/j.chaos.2025.116012","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116012","url":null,"abstract":"Memristors play an important role in the modeling of neural networks as external stimuli for neuron excitation and biological synapses for information exchange. Recently, the discrete fracmemristor has shown excellent properties in describing the memory effect of nonlinear systems, including biological nervous systems. In this paper, we propose a fractional memristive Rulkov neuron model (FMRN) by introducing the fractional discrete HP-type memristor (FDM-HP) into a single fractional Rulkov neuron (FRN) as electromagnetic radiation. Their parametric modulation dynamics are investigated and compared by means of firing patterns, Lyapunov exponents, bifurcation diagrams and complexity. In addition, to verify the information transfer ability of discrete fracmemristor as a synaptic model, a fractional bi-neuron system is constructed by coupling two FRNs with FDM-HP, which is further subjected to the analyses of phase synchronization and firing behaviors. The simulation results show that the combination of FDM-HP and FRN can effectively enrich the dynamics of neuron system, achieve synchronous firing rhythms, and generate various novel firing patterns. The researches provide the theoretical and experimental supports for neuronal modeling and synapse-based synchronization, which lay the foundation for further researches on complex neural networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"40 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987823","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.116022
Nidhal Ben Khedher, Zia Ullah, Md. Mahbub Alam, Bagh Ali, Saleh Al Arni, Mouldi Ben Amara, Mohamed Boujelbene
This work based on oscillation, fluctuation, periodic and transient analysis of heat and mass transmission of Casson nanofluid motion over a stretched surface with radiation, buoyancy force and entropy optimization. This problem is very useful in energy insulation, coating, energy conversion, climate, and ecological systems. The entropy generation and thermal radiations are applied to enhance the heat transmission of Casson nanomaterial. Periodic mathematical expressions are developed for this problem. Dimensionless variables, oscillatory-stokes formulation and primitive transformation are utilized to develop similarity in coding in FORTRAN language. Implicit finite difference methodology is applied for numerical outcomes in the presence of Gaussian elimination scheme. The computational outputs of velocity variation, energy and concentration graphs through different parameters are depicted. The steady as well as oscillatory form of skin friction and heat-mass transportation is depicted. The high magnitude in fluid velocity and temperature function is depicted with maximum entropy generation, Casson and radiation effects. The steady magnitude of heat and mass transportation is increased with Brownian motion and thermophoresis effects. The oscillation, amplitude and periodical waves in heat and mass transmission are increased with high Prandtl and Schmidt numbers.
{"title":"Significance of fluctuating amplitude and turbulence on nonlinear radiative heat transfer in Casson nanofluid using primitive and Stokes transformation","authors":"Nidhal Ben Khedher, Zia Ullah, Md. Mahbub Alam, Bagh Ali, Saleh Al Arni, Mouldi Ben Amara, Mohamed Boujelbene","doi":"10.1016/j.chaos.2025.116022","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116022","url":null,"abstract":"This work based on oscillation, fluctuation, periodic and transient analysis of heat and mass transmission of Casson nanofluid motion over a stretched surface with radiation, buoyancy force and entropy optimization. This problem is very useful in energy insulation, coating, energy conversion, climate, and ecological systems. The entropy generation and thermal radiations are applied to enhance the heat transmission of Casson nanomaterial. Periodic mathematical expressions are developed for this problem. Dimensionless variables, oscillatory-stokes formulation and primitive transformation are utilized to develop similarity in coding in FORTRAN language. Implicit finite difference methodology is applied for numerical outcomes in the presence of Gaussian elimination scheme. The computational outputs of velocity variation, energy and concentration graphs through different parameters are depicted. The steady as well as oscillatory form of skin friction and heat-mass transportation is depicted. The high magnitude in fluid velocity and temperature function is depicted with maximum entropy generation, Casson and radiation effects. The steady magnitude of heat and mass transportation is increased with Brownian motion and thermophoresis effects. The oscillation, amplitude and periodical waves in heat and mass transmission are increased with high Prandtl and Schmidt numbers.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"29 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987822","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.115993
Jiaqi Li, Zhenfu Li, Xinli Qi
The interregional transportation networks (ITNs) have a significant impact on regional population movement, trade flow and economic development. Compared to single-layer networks, multilayer networks theory can help ITNs to capture more detailed information applied to transportation plan, design and management. Despite the growing interest in studying ITNs using multilayer network analysis, attempts to document and better understand this area have largely remained elusive. To fill the gap, this article provides a comprehensive bibliometric assessment of multilayer networks-based ITNs analysis. Three research aspects, including the construction, characteristics, and functions of ITNs analysis based on multilayer networks theory has been systematically reviewed. Through analysis, research on multilayer networks-based ITNs are expanding from aviation networks to other ITNs and evolving from static to dynamic networks. In the future, advancements are expected in the establishment of interlayer relationships, the development of composite ITNs, effective management of dynamic network risk propagation, and enhancement of system robustness.
{"title":"A review of multilayer networks-based interregional transportation networks analysis","authors":"Jiaqi Li, Zhenfu Li, Xinli Qi","doi":"10.1016/j.chaos.2025.115993","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.115993","url":null,"abstract":"The interregional transportation networks (ITNs) have a significant impact on regional population movement, trade flow and economic development. Compared to single-layer networks, multilayer networks theory can help ITNs to capture more detailed information applied to transportation plan, design and management. Despite the growing interest in studying ITNs using multilayer network analysis, attempts to document and better understand this area have largely remained elusive. To fill the gap, this article provides a comprehensive bibliometric assessment of multilayer networks-based ITNs analysis. Three research aspects, including the construction, characteristics, and functions of ITNs analysis based on multilayer networks theory has been systematically reviewed. Through analysis, research on multilayer networks-based ITNs are expanding from aviation networks to other ITNs and evolving from static to dynamic networks. In the future, advancements are expected in the establishment of interlayer relationships, the development of composite ITNs, effective management of dynamic network risk propagation, and enhancement of system robustness.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"30 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988177","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 : 2025-01-16DOI: 10.1016/j.chaos.2025.115988
Xuegeng Mao, Chengliang Xia, Jinzhao Liu, Hang Zhang, Yuming Ding, Yongming Yao, Zezhou Liu
In this paper, we first propose dispersion transition entropy (DTE) to measure inner dynamical complexity of signals or time series from the perspective of states transition between consecutive dispersion patterns, and then introduce a new similarity measure based upon the Jensen–Fisher divergence (JFD) between dispersion-transition distributions. The numerical experiments prove that DTE is immune to the data length but more sensitive to the state or characteristic changes compared with traditional dispersion entropy. In addition, the results of tests on white noise and 1/f noise are consistent with the complexity theory in present researches. Then the new similarity measure exhibits superior performances on distinguishing chaotic time series from stochastic processes since JFD enlarges the local difference or changes between dispersion-transition matrices. Especially, for the axle box acceleration vibration signals of rail detection, the dispersion-transition distributions of normal, rail corrugation and impact signals are significantly dissimilar. By estimating the JFD between the probability distributions of two successive sliding windows, rail corrugation and impact defects can be identified and located.
{"title":"A novel similarity measure based on dispersion-transition matrix and Jensen–Fisher divergence and its application on the detection of rail short-wave defects","authors":"Xuegeng Mao, Chengliang Xia, Jinzhao Liu, Hang Zhang, Yuming Ding, Yongming Yao, Zezhou Liu","doi":"10.1016/j.chaos.2025.115988","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.115988","url":null,"abstract":"In this paper, we first propose dispersion transition entropy (DTE) to measure inner dynamical complexity of signals or time series from the perspective of states transition between consecutive dispersion patterns, and then introduce a new similarity measure based upon the Jensen–Fisher divergence (JFD) between dispersion-transition distributions. The numerical experiments prove that DTE is immune to the data length but more sensitive to the state or characteristic changes compared with traditional dispersion entropy. In addition, the results of tests on white noise and 1/f noise are consistent with the complexity theory in present researches. Then the new similarity measure exhibits superior performances on distinguishing chaotic time series from stochastic processes since JFD enlarges the local difference or changes between dispersion-transition matrices. Especially, for the axle box acceleration vibration signals of rail detection, the dispersion-transition distributions of normal, rail corrugation and impact signals are significantly dissimilar. By estimating the JFD between the probability distributions of two successive sliding windows, rail corrugation and impact defects can be identified and located.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"30 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988178","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 : 2025-01-15DOI: 10.1016/j.chaos.2025.116006
Li-Na Lian, Xiang-Ping Yan, Cun-Hua Zhang
This paper is concerned with a bimolecular reaction–diffusion model with saturation law and cross-diffusion and subject to Neumann boundary conditions. Firstly, both the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of the positive constant steady state of model are established through the linearization analysis. Secondly, the amplitude equations of model in proximity to the positive constant steady state are obtained by means of the method of multiple-scale time perturbation analysis and successive approximations as the bifurcation parameters are confined to the interior of Turing instability region and near Turing bifurcation curve. Thirdly, the classification and stability of Turing patterns in the diffusion bimolecular model are analyzed based on the existence and stability of the stationary solutions to the amplitude equations. It is found that the appearance of spatial diffusion in the bimolecular chemical reaction model with saturation law can give rise to nonuniform spatial patterns and lead to more complex dynamical behaviors. When the bifurcation parameters are confined to the interior of Turing instability region and near Turing bifurcation curve, the spot patterns, the strap (maze) patterns as well as the mixture of spot and strap patterns can occur. Theoretical findings show that suitable reaction–diffusion systems can be used to explain the mechanism in formation of patterns in the natural world. Finally, in order to substantiate our theoretical findings, some suitable numerical simulations are also provided according to Matlab software package and difference methods solving the approximate solutions of partial differential equations of parabolic types.
{"title":"Pattern dynamics in a bimolecular reaction–diffusion model with saturation law and cross-diffusion","authors":"Li-Na Lian, Xiang-Ping Yan, Cun-Hua Zhang","doi":"10.1016/j.chaos.2025.116006","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.116006","url":null,"abstract":"This paper is concerned with a bimolecular reaction–diffusion model with saturation law and cross-diffusion and subject to Neumann boundary conditions. Firstly, both the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of the positive constant steady state of model are established through the linearization analysis. Secondly, the amplitude equations of model in proximity to the positive constant steady state are obtained by means of the method of multiple-scale time perturbation analysis and successive approximations as the bifurcation parameters are confined to the interior of Turing instability region and near Turing bifurcation curve. Thirdly, the classification and stability of Turing patterns in the diffusion bimolecular model are analyzed based on the existence and stability of the stationary solutions to the amplitude equations. It is found that the appearance of spatial diffusion in the bimolecular chemical reaction model with saturation law can give rise to nonuniform spatial patterns and lead to more complex dynamical behaviors. When the bifurcation parameters are confined to the interior of Turing instability region and near Turing bifurcation curve, the spot patterns, the strap (maze) patterns as well as the mixture of spot and strap patterns can occur. Theoretical findings show that suitable reaction–diffusion systems can be used to explain the mechanism in formation of patterns in the natural world. Finally, in order to substantiate our theoretical findings, some suitable numerical simulations are also provided according to Matlab software package and difference methods solving the approximate solutions of partial differential equations of parabolic types.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"13 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142988181","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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