Pub Date : 2026-01-06DOI: 10.1016/j.chaos.2025.117843
Chunlong Zhou , Han Bao , Yunzhen Zhang , Xi Zhang , Bocheng Bao
It has been documented that using non-monotonic activation functions in neural networks can expand their memory capacity, and their performance is superior to that of traditional ones that only use monotonic activation functions. This study proposes a three-neuron sine activated Hopfield neural network (SA-HNN) without self-connections, and explores its multi-stable dynamics induced by the sine activation function, demonstrating the expansion of memory capacity. The boundedness and ultimate boundedness are proved, and the equilibria with stability are analyzed. Using numerical methods, the synaptic weights related bifurcation behaviors under different initial states are investigated. The results show that SA-HNN can present up to 14 heterogeneous coexistence attractors, far more than the number found in HNNs using other activation functions, manifesting that the sine activation function indeed expands the memory capacity of HNNs. Finally, an analog circuit is designed and hardware experiments are performed to acquire various coexistence attractors, thereby validating the numerical results.
{"title":"Memory capacity expansion in a sine activated Hopfield neural network","authors":"Chunlong Zhou , Han Bao , Yunzhen Zhang , Xi Zhang , Bocheng Bao","doi":"10.1016/j.chaos.2025.117843","DOIUrl":"10.1016/j.chaos.2025.117843","url":null,"abstract":"<div><div>It has been documented that using non-monotonic activation functions in neural networks can expand their memory capacity, and their performance is superior to that of traditional ones that only use monotonic activation functions. This study proposes a three-neuron sine activated Hopfield neural network (SA-HNN) without self-connections, and explores its multi-stable dynamics induced by the sine activation function, demonstrating the expansion of memory capacity. The boundedness and ultimate boundedness are proved, and the equilibria with stability are analyzed. Using numerical methods, the synaptic weights related bifurcation behaviors under different initial states are investigated. The results show that SA-HNN can present up to 14 heterogeneous coexistence attractors, far more than the number found in HNNs using other activation functions, manifesting that the sine activation function indeed expands the memory capacity of HNNs. Finally, an analog circuit is designed and hardware experiments are performed to acquire various coexistence attractors, thereby validating the numerical results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117843"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921920","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 : 2026-01-06DOI: 10.1016/j.chaos.2025.117852
Kaijie Chen , Zhijun Li , Yang Yin , Mengjiao Wang
Astrocytes actively participate in neural information processing and modulate multiple surrounding neurons through a “one-to-many” regulatory mechanism. To explore this interaction, we propose an astrocyte-mediated Hopfield neural network (AmHNN) model that captures the essential coupling structure of biological neural networks. Linear stability analysis reveals that astrocyte feedback can shift the network's equilibrium point, thereby modifying the Jacobian matrix and its eigenvalues. This reshapes the network's stability landscape and provides a theoretical basis for the emergence of complex rhythms, including chaos and hyper-chaos. Comparative analysis with models lacking the astrocyte or the third neuron indicates that AmHNN is not merely an expansion of the network dimension; its rich dynamic characteristics better mimic the firing rhythm of biological neural networks. By tuning astrocyte feedback intensities and internal parameters, we quantitatively characterize astrocyte-induced variations in network stability and derive a Hamiltonian energy function. This reveals how astrocyte feedback modulates the rate and magnitude of energy injection to drive transitions in network firing dynamics. A DSP-based hardware implementation, evaluated using a multidimensional framework involving NRMSE and Pearson correlation, demonstrates strong agreement with numerical simulations. These findings deepen the deepen understanding of neuron-astrocyte interactions, thereby offering a novel paradigm for advancing neuromorphic computing, secure communications, and brain-inspired intelligence.
{"title":"Astrocyte-mediated Hopfield Neural Network: modeling, dynamical analysis, and hardware implementation","authors":"Kaijie Chen , Zhijun Li , Yang Yin , Mengjiao Wang","doi":"10.1016/j.chaos.2025.117852","DOIUrl":"10.1016/j.chaos.2025.117852","url":null,"abstract":"<div><div>Astrocytes actively participate in neural information processing and modulate multiple surrounding neurons through a “one-to-many” regulatory mechanism. To explore this interaction, we propose an astrocyte-mediated Hopfield neural network (AmHNN) model that captures the essential coupling structure of biological neural networks. Linear stability analysis reveals that astrocyte feedback can shift the network's equilibrium point, thereby modifying the Jacobian matrix and its eigenvalues. This reshapes the network's stability landscape and provides a theoretical basis for the emergence of complex rhythms, including chaos and hyper-chaos. Comparative analysis with models lacking the astrocyte or the third neuron indicates that AmHNN is not merely an expansion of the network dimension; its rich dynamic characteristics better mimic the firing rhythm of biological neural networks. By tuning astrocyte feedback intensities and internal parameters, we quantitatively characterize astrocyte-induced variations in network stability and derive a Hamiltonian energy function. This reveals how astrocyte feedback modulates the rate and magnitude of energy injection to drive transitions in network firing dynamics. A DSP-based hardware implementation, evaluated using a multidimensional framework involving NRMSE and Pearson correlation, demonstrates strong agreement with numerical simulations. These findings deepen the deepen understanding of neuron-astrocyte interactions, thereby offering a novel paradigm for advancing neuromorphic computing, secure communications, and brain-inspired intelligence.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117852"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922000","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 : 2026-01-06DOI: 10.1016/j.chaos.2026.117871
Ana C. Díaz Bacca , Pablo M. Rodriguez , Catalina M. Rúa-Alvarez
We consider a rumor model in which the network is divided into three classes of agents: ignorant, spreader, and stifler. A spreader transmits the rumor to each of its ignorant neighbors at rate one, and at the same rate, it becomes a stifler after interacting with other spreaders or stiflers. The overall process is described by a continuous-time Markov chain that represents the state of each node at any given time. The underlying network is a ring lattice with nodes, where each node is connected to its nearest neighbors. This structure has often been used as the foundation for small-world network models, which are typically generated by rewiring or adding edges to introduce shortcuts. It is well known that when a rumor process takes place on such modified networks, the system undergoes a transition between localization and propagation at a finite mean degree. This transition illustrates the strong influence of shortcuts on the spreading of information. In this work, we adopt a complementary perspective by focusing on the rumor process within the pure ring lattice, without adding any shortcuts. Our aim is to show that even in this simplified setting, the model can exhibit behavior regarding the proportion of nodes reached by the rumor that is comparable to what is observed in homogeneously mixed populations. To this end, we identify the value of as a function of for which this behavior emerges and demonstrate that it scales as . Our conclusions are drawn from the analysis of contrasting examples and from a broader examination of the general case through numerical simulations.
{"title":"How far can a rumor travel without shortcuts?","authors":"Ana C. Díaz Bacca , Pablo M. Rodriguez , Catalina M. Rúa-Alvarez","doi":"10.1016/j.chaos.2026.117871","DOIUrl":"10.1016/j.chaos.2026.117871","url":null,"abstract":"<div><div>We consider a rumor model in which the network is divided into three classes of agents: ignorant, spreader, and stifler. A spreader transmits the rumor to each of its ignorant neighbors at rate one, and at the same rate, it becomes a stifler after interacting with other spreaders or stiflers. The overall process is described by a continuous-time Markov chain that represents the state of each node at any given time. The underlying network is a ring lattice with <span><math><mi>n</mi></math></span> nodes, where each node is connected to its <span><math><mrow><mn>2</mn><mi>k</mi></mrow></math></span> nearest neighbors. This structure has often been used as the foundation for small-world network models, which are typically generated by rewiring or adding edges to introduce shortcuts. It is well known that when a rumor process takes place on such modified networks, the system undergoes a transition between localization and propagation at a finite mean degree. This transition illustrates the strong influence of shortcuts on the spreading of information. In this work, we adopt a complementary perspective by focusing on the rumor process within the pure ring lattice, without adding any shortcuts. Our aim is to show that even in this simplified setting, the model can exhibit behavior regarding the proportion of nodes reached by the rumor that is comparable to what is observed in homogeneously mixed populations. To this end, we identify the value of <span><math><mi>k</mi></math></span> as a function of <span><math><mi>n</mi></math></span> for which this behavior emerges and demonstrate that it scales as <span><math><mrow><mo>log</mo><mi>n</mi></mrow></math></span>. Our conclusions are drawn from the analysis of contrasting examples and from a broader examination of the general case through numerical simulations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117871"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902628","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 : 2026-01-05DOI: 10.1016/j.chaos.2026.117869
Xianchen Wang , Shivakumar Rajagopal , Shihong Dang , Rui Yang , Fatemeh Parastesh
Explosive synchronization represents an abrupt and hysteretic transition to collective neural activity and has been linked to sudden functional changes in brain dynamics. In this work, we systematically investigate how different synaptic mechanisms shape explosive synchronization in heterogeneous networks of Chialvo neurons. By comparing electrical, chemical, and hybrid synaptic interactions, we reveal pronounced qualitative differences in their synchronization behavior. Our results show that electrical coupling robustly supports explosive synchronization across a wide range of conditions, whereas chemical synapses exhibit a significantly lower probability of explosive transitions and reduced hysteresis. Neuronal heterogeneity enhances explosiveness under electrical coupling but suppresses it in chemically coupled networks. We further demonstrate that synaptic reversal potential plays a decisive role: fully inhibitory chemical networks fail to synchronize, while increasing excitatory drive lowers the synchronization threshold and weakens bistability. Synaptic delay introduces additional control, enabling both explosive and continuous transitions depending on its value. In hybrid networks, intermediate ratios of electrical and chemical coupling eliminate explosive synchronization altogether, yielding smooth and reversible transitions. Finally, increasing connectivity density progressively destroys explosive synchronization, with chemical synapses showing much higher sensitivity to topology than electrical ones.
{"title":"Explosive synchronization in Chialvo neuronal network: Roles of chemical, electrical, and hybrid coupling","authors":"Xianchen Wang , Shivakumar Rajagopal , Shihong Dang , Rui Yang , Fatemeh Parastesh","doi":"10.1016/j.chaos.2026.117869","DOIUrl":"10.1016/j.chaos.2026.117869","url":null,"abstract":"<div><div>Explosive synchronization represents an abrupt and hysteretic transition to collective neural activity and has been linked to sudden functional changes in brain dynamics. In this work, we systematically investigate how different synaptic mechanisms shape explosive synchronization in heterogeneous networks of Chialvo neurons. By comparing electrical, chemical, and hybrid synaptic interactions, we reveal pronounced qualitative differences in their synchronization behavior. Our results show that electrical coupling robustly supports explosive synchronization across a wide range of conditions, whereas chemical synapses exhibit a significantly lower probability of explosive transitions and reduced hysteresis. Neuronal heterogeneity enhances explosiveness under electrical coupling but suppresses it in chemically coupled networks. We further demonstrate that synaptic reversal potential plays a decisive role: fully inhibitory chemical networks fail to synchronize, while increasing excitatory drive lowers the synchronization threshold and weakens bistability. Synaptic delay introduces additional control, enabling both explosive and continuous transitions depending on its value. In hybrid networks, intermediate ratios of electrical and chemical coupling eliminate explosive synchronization altogether, yielding smooth and reversible transitions. Finally, increasing connectivity density progressively destroys explosive synchronization, with chemical synapses showing much higher sensitivity to topology than electrical ones.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117869"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902633","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 : 2026-01-05DOI: 10.1016/j.chaos.2026.117860
R. Abouem A Ribama , Z.I. Djoufack , J.P. Nguenang
Carbon nanotubes are nanostructures renowned for their remarkable mechanical, electrical, and thermal properties, with their vibrational dynamics playing a central role in their stability and functionality. This article presents an in-depth modeling of the quantum vibrational dynamics of two-dimensional carbon nanotubes. By developing an anharmonic discrete Hamiltonian and then quantizing it using bosonic operators, a nonlinear two-dimensional Schrödinger equation is derived. This equation allows for the study of the formation, stability, and dynamics of quantum localized vibrational modes. The results show that the stability of these modes strongly depends on the parameters of linear and nonlinear coupling, particularly the local rigidity and anharmonic interactions. Modulating these parameters provides precise control over the localization, dissipation, and collisions of breathers, enabling manipulation of vibrational excitations at the nanometric scale. Analytical and numerical analyses also reveal the emergence of energy confinement phenomena and controlled dissipation. Furthermore, the numerical study of breather collisions highlights complex dynamics such as trapping, energy barriers, excitation, and the formation of energy wells which depend on the ratio between the local nonlinear parameter and the inter-site nonlinear parameter. This work provides a deeper understanding of nonlinear phenomena at the nanoscale, opening avenues for precise control of vibrational excitations in carbon nanotubes, with potential applications in energy management, nanoelectronics, and nanomechanics.
{"title":"Nonlinear vibrational dynamics and stability of quantum intrinsic localized modes in carbon nanotubes: Influence of harmonic and nonlinear coupling parameters","authors":"R. Abouem A Ribama , Z.I. Djoufack , J.P. Nguenang","doi":"10.1016/j.chaos.2026.117860","DOIUrl":"10.1016/j.chaos.2026.117860","url":null,"abstract":"<div><div>Carbon nanotubes are nanostructures renowned for their remarkable mechanical, electrical, and thermal properties, with their vibrational dynamics playing a central role in their stability and functionality. This article presents an in-depth modeling of the quantum vibrational dynamics of two-dimensional carbon nanotubes. By developing an anharmonic discrete Hamiltonian and then quantizing it using bosonic operators, a nonlinear two-dimensional Schrödinger equation is derived. This equation allows for the study of the formation, stability, and dynamics of quantum localized vibrational modes. The results show that the stability of these modes strongly depends on the parameters of linear and nonlinear coupling, particularly the local rigidity and anharmonic interactions. Modulating these parameters provides precise control over the localization, dissipation, and collisions of breathers, enabling manipulation of vibrational excitations at the nanometric scale. Analytical and numerical analyses also reveal the emergence of energy confinement phenomena and controlled dissipation. Furthermore, the numerical study of breather collisions highlights complex dynamics such as trapping, energy barriers, excitation, and the formation of energy wells which depend on the ratio between the local nonlinear parameter and the inter-site nonlinear parameter. This work provides a deeper understanding of nonlinear phenomena at the nanoscale, opening avenues for precise control of vibrational excitations in carbon nanotubes, with potential applications in energy management, nanoelectronics, and nanomechanics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117860"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145897475","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 : 2026-01-05DOI: 10.1016/j.chaos.2026.117863
I. Andrade , D. Bazeia , M.A. Marques , R. Menezes
We investigate novel structures which arise from the compactification of vacuumless kinks in scalar field models coupled to impurities that preserve half the BPS sectors, described by first-order equations. We also investigate the behavior of the energy density and linear stability of the solutions. We show that compact vacuumless kinks cannot be obtained in impurity-free canonical models. By considering two distinct impurities, we study the conditions needed to induce compactification. In this scenario, stable half-compact or compact solutions are shown to emerge from the systems.
{"title":"Compact structures in impurity-doped vacuumless systems","authors":"I. Andrade , D. Bazeia , M.A. Marques , R. Menezes","doi":"10.1016/j.chaos.2026.117863","DOIUrl":"10.1016/j.chaos.2026.117863","url":null,"abstract":"<div><div>We investigate novel structures which arise from the compactification of vacuumless kinks in scalar field models coupled to impurities that preserve half the BPS sectors, described by first-order equations. We also investigate the behavior of the energy density and linear stability of the solutions. We show that compact vacuumless kinks cannot be obtained in impurity-free canonical models. By considering two distinct impurities, we study the conditions needed to induce compactification. In this scenario, stable half-compact or compact solutions are shown to emerge from the systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117863"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145897476","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 : 2026-01-05DOI: 10.1016/j.chaos.2025.117840
Dhrubajyoti Biswas, Arpan Banerjee
Complex physical systems are often governed by interactions that extend beyond pairwise links, underscoring the need to establish a map between interpretable system parameters and emergent synchronisation phenomena in hyper-graphs. To achieve this, the current work formulates an adaptive Kuramoto model that incorporates hyperedges of arbitrary order and explores their effects on synchronisation. By deriving the exact order parameter dynamics in the thermodynamic limit, analytical expressions governing the collective dynamics are obtained. Subsequent numerics confirm the analytical predictions, in addition to capturing qualitatively different dynamical regimes and phase transitions. Further investigations based on numerically constructed order parameter distributions demonstrate how fluctuations due to finite system size can influence the long-term system dynamics by inducing spontaneous transitions. These results provide important insights and can have diverse applications, such as designing optimal surgical procedures for drug-resistant epilepsy in the human brain and identifying the sources of rumours in social networks.
{"title":"Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions","authors":"Dhrubajyoti Biswas, Arpan Banerjee","doi":"10.1016/j.chaos.2025.117840","DOIUrl":"10.1016/j.chaos.2025.117840","url":null,"abstract":"<div><div>Complex physical systems are often governed by interactions that extend beyond pairwise links, underscoring the need to establish a map between interpretable system parameters and emergent synchronisation phenomena in hyper-graphs. To achieve this, the current work formulates an adaptive Kuramoto model that incorporates hyperedges of arbitrary order and explores their effects on synchronisation. By deriving the exact order parameter dynamics in the thermodynamic limit, analytical expressions governing the collective dynamics are obtained. Subsequent numerics confirm the analytical predictions, in addition to capturing qualitatively different dynamical regimes and phase transitions. Further investigations based on numerically constructed order parameter distributions demonstrate how fluctuations due to finite system size can influence the long-term system dynamics by inducing spontaneous transitions. These results provide important insights and can have diverse applications, such as designing optimal surgical procedures for drug-resistant epilepsy in the human brain and identifying the sources of rumours in social networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117840"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145897239","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 : 2026-01-05DOI: 10.1016/j.chaos.2025.117836
Huimin Qi , Fengjun Li , Fuqiang Wu , Xinlei An
Neuronal circuits involving two capacitors have an essential role in exploring biophysical mechanisms and mimicking brain-inspired devices. Given the dual-capacitor effect in nerve cells, we systematically investigate dynamical characteristics of the bi-membrane neuron-like (BMN) circuit subjected to a constant current source and alternating magnetic stimulus based on a magnetoelectric nonlinear metamaterial (MNM). Different from traditional single-membrane designs, the BMN circuit has a variety of rich structure, supporting more complex biological dynamics for enhanced neuromorphic computation. Through theoretical analysis and numerical simulation, it is found that the BMN circuit with an increased constant current exhibits neuronal excitability associated with a Hopf bifurcation. Based on Helmholtz's law, the energy function of the BMN circuit system is verified. Under the alternating magnetic stimulus, the BMN circuit can reproduce a chaotic bursting pattern by using numerical simulation. Finally, a BMN circuit network model with constant current source and alternating magnetic stimulus is constructed under resistive coupling. Using a master stability function (MSF) method, it is demonstrated that the BMN circuit network with chaotic and chaotic bursting patterns can achieve stable synchronization under suitable coupling parameters, and the regulation mechanism of coupling strength is elucidated. This study enriches the dynamic theory of the BMN circuit, providing a theoretical reference and practical guidance for network synchronization control and neuromorphic device design.
{"title":"Bursting synchronization and excitability of the bi-membrane neuron-like circuit under electromagnetic stimuli","authors":"Huimin Qi , Fengjun Li , Fuqiang Wu , Xinlei An","doi":"10.1016/j.chaos.2025.117836","DOIUrl":"10.1016/j.chaos.2025.117836","url":null,"abstract":"<div><div>Neuronal circuits involving two capacitors have an essential role in exploring biophysical mechanisms and mimicking brain-inspired devices. Given the dual-capacitor effect in nerve cells, we systematically investigate dynamical characteristics of the bi-membrane neuron-like (BMN) circuit subjected to a constant current source and alternating magnetic stimulus based on a magnetoelectric nonlinear metamaterial (MNM). Different from traditional single-membrane designs, the BMN circuit has a variety of rich structure, supporting more complex biological dynamics for enhanced neuromorphic computation. Through theoretical analysis and numerical simulation, it is found that the BMN circuit with an increased constant current exhibits neuronal excitability associated with a Hopf bifurcation. Based on Helmholtz's law, the energy function of the BMN circuit system is verified. Under the alternating magnetic stimulus, the BMN circuit can reproduce a chaotic bursting pattern by using numerical simulation. Finally, a BMN circuit network model with constant current source and alternating magnetic stimulus is constructed under resistive coupling. Using a master stability function (MSF) method, it is demonstrated that the BMN circuit network with chaotic and chaotic bursting patterns can achieve stable synchronization under suitable coupling parameters, and the regulation mechanism of coupling strength is elucidated. This study enriches the dynamic theory of the BMN circuit, providing a theoretical reference and practical guidance for network synchronization control and neuromorphic device design.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117836"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902632","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 : 2026-01-05DOI: 10.1016/j.chaos.2025.117848
Yufeng Xie , Chang Shu , Shirong Liu , Shiwen Sun , Jing Wang , Pei Ye , Yadong Yan
Previous studies on cascade failures in interdependent networks have primarily focused on nodes. However, in real-world scenarios, interactions between networks are established through connecting edges rather than the nodes themselves, leading to the concept of edge-coupled interdependent networks (EIN). In this paper, we extend the model to multilayer edge-coupled interdependent networks (MEIN) by reinforcing a fraction m of the connecting edges. We analyze the phase transition behavior in these reinforced networks. The reinforcement of a subset of edges is shown to lower the critical threshold and alter the nature of the phase transition from first-order to mixed. Our results demonstrate that strategically enhancing a certain proportion of interconnecting edges can significantly improve the robustness of multilayer edge-coupled interdependent networks.
{"title":"Research on the robustness of multi-layer interdependent networks based on edge-preserving strategies","authors":"Yufeng Xie , Chang Shu , Shirong Liu , Shiwen Sun , Jing Wang , Pei Ye , Yadong Yan","doi":"10.1016/j.chaos.2025.117848","DOIUrl":"10.1016/j.chaos.2025.117848","url":null,"abstract":"<div><div>Previous studies on cascade failures in interdependent networks have primarily focused on nodes. However, in real-world scenarios, interactions between networks are established through connecting edges rather than the nodes themselves, leading to the concept of edge-coupled interdependent networks (EIN). In this paper, we extend the model to multilayer edge-coupled interdependent networks (MEIN) by reinforcing a fraction m of the connecting edges. We analyze the phase transition behavior in these reinforced networks. The reinforcement of a subset of edges is shown to lower the critical threshold and alter the nature of the phase transition from first-order to mixed. Our results demonstrate that strategically enhancing a certain proportion of interconnecting edges can significantly improve the robustness of multilayer edge-coupled interdependent networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117848"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902635","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 : 2026-01-05DOI: 10.1016/j.chaos.2025.117782
Haohao Guo , Xiaobin Xu , Leilei Chang , Haiquan Wang , Runkai Li , Wanjie Zhou
In Dempster-Shafer (DS) evidence theory, the basic probability assignment function (i.e., “evidence” provided by an information source) is used to model uncertain information, and Dempster's combination rule is employed to fuse multiple pieces of evidence to obtain a more reliable comprehensive result for decision-making. However, when there is a high degree of conflict between two pieces of evidence, the fused result may be counter-intuitive, thereby deteriorating decision accuracy. Hence, constructing appropriate similarity measures to quantify the degree of conflict between two pieces of evidence becomes crucial for resolving these counter-intuitive outcomes. Currently, traditional similarity measures (S) are predominantly obtained through a linear transformation of evidence distance (d). For instance, the similarity between two pieces of evidence is calculated as “S = 1-d”. Such simplistic “univariate” linear transformations suffer from limitations like insufficient precision and poor adaptability. Therefore, this paper proposes a novel binary composite evidence similarity measure. In the transformation process, two distinct mapping attitudes of “optimistic” and “pessimistic” are considered, and the corresponding parameters are given to adjust to the change trend of the two attitudes. In addition, we theoretically prove that the proposed binary composite measure satisfies the core properties of similarity measures (non-negativity, symmetry, boundedness, non-degeneracy, positive monotonicity, and extreme conflict). Finally, the proposed measure is compared and analyzed with mainstream similarity measures through multiple representative numerical cases and application cases in specialized fields such as fault diagnosis and target recognition. The experimental results validate the superiority of the proposed measure in terms of measurement accuracy.
{"title":"A novel binary composite similarity measure with optimistic and pessimistic attitudes for evidence fusion","authors":"Haohao Guo , Xiaobin Xu , Leilei Chang , Haiquan Wang , Runkai Li , Wanjie Zhou","doi":"10.1016/j.chaos.2025.117782","DOIUrl":"10.1016/j.chaos.2025.117782","url":null,"abstract":"<div><div>In Dempster-Shafer (DS) evidence theory, the basic probability assignment function (i.e., “evidence” provided by an information source) is used to model uncertain information, and Dempster's combination rule is employed to fuse multiple pieces of evidence to obtain a more reliable comprehensive result for decision-making. However, when there is a high degree of conflict between two pieces of evidence, the fused result may be counter-intuitive, thereby deteriorating decision accuracy. Hence, constructing appropriate similarity measures to quantify the degree of conflict between two pieces of evidence becomes crucial for resolving these counter-intuitive outcomes. Currently, traditional similarity measures (<em>S</em>) are predominantly obtained through a linear transformation of evidence distance (<em>d</em>). For instance, the similarity between two pieces of evidence is calculated as “<em>S</em> = 1-<em>d</em>”. Such simplistic “univariate” linear transformations suffer from limitations like insufficient precision and poor adaptability. Therefore, this paper proposes a novel binary composite evidence similarity measure. In the transformation process, two distinct mapping attitudes of “optimistic” and “pessimistic” are considered, and the corresponding parameters are given to adjust to the change trend of the two attitudes. In addition, we theoretically prove that the proposed binary composite measure satisfies the core properties of similarity measures (non-negativity, symmetry, boundedness, non-degeneracy, positive monotonicity, and extreme conflict). Finally, the proposed measure is compared and analyzed with mainstream similarity measures through multiple representative numerical cases and application cases in specialized fields such as fault diagnosis and target recognition. The experimental results validate the superiority of the proposed measure in terms of measurement accuracy.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117782"},"PeriodicalIF":5.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145897334","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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