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When moving away reduces polarization: Selective depolarization by endogenous migration in attraction–repulsion opinion dynamics 当移动远离减少极化:选择性去极化通过内生迁移在吸引-排斥意见动态
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-23 DOI: 10.1016/j.chaos.2026.118128
Hong Zhang
Opinion polarization poses a fundamental challenge for contemporary societies, yet how spatial mobility coevolves with attraction–repulsion influence remains poorly understood. We develop an agent-based model in continuous two-dimensional space that couples tolerance-based attraction–repulsion opinion updates with endogenous migration: agents interact locally and then move toward ideologically similar neighbors while avoiding dissimilar ones. Extensive parameter sweeps show that mobility acts as a selective depolarizer. Above a critical tolerance threshold, mobility suppresses repulsion-driven extremization by enabling agents to leave antagonistic neighborhoods before repeated hostile encounters accumulate. At the same time, mobility strengthens spatial assortativity, yielding a robust depolarized segregation regime in which ideological polarization remains low while spatial clustering is high—demonstrating that echo-chamber-like structure need not coincide with ideological extremism. Across conditions, tolerance sets the dominant phase boundary, whereas exposure, interaction radius, and movement speed primarily modulate transition locations and time scales. As a mechanistic model, these results highlight a trade-off between reduced extremization and reduced cross-cutting contact, and suggest that interventions focusing only on mobility or exposure may have limited impact when tolerance is low; linking model parameters to concrete policy levers requires empirical calibration.
意见两极分化对当代社会构成了根本性的挑战,然而空间流动性如何与吸引-排斥影响共同演变仍然知之甚少。我们在连续二维空间中开发了一个基于智能体的模型,该模型将基于容忍度的吸引-排斥意见更新与内生迁移结合在一起:智能体在局部相互作用,然后向意识形态相似的邻居移动,同时避开不相似的邻居。广泛的参数扫描表明,迁移率起着选择性去极化的作用。在临界容忍度阈值以上,移动性抑制排斥驱动的极端化,使代理人在反复的敌对遭遇积累之前离开敌对社区。与此同时,流动性增强了空间协调性,形成了一种强大的去极化隔离制度,在这种制度下,意识形态两极分化程度较低,而空间集聚程度较高——这表明类似回声室的结构不一定与意识形态极端主义一致。在各种条件下,容差设定了主要的相边界,而曝光、相互作用半径和运动速度主要调节过渡位置和时间尺度。作为一个机制模型,这些结果强调了减少极端化和减少交叉接触之间的权衡,并表明仅关注流动性或暴露的干预措施在耐受性低时可能影响有限;将模型参数与具体的政策杠杆联系起来需要经验校准。
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引用次数: 0
Caputo–Orlicz framework for functions of bounded Ψ-variation and exact fractal dimensions of their graphs 有界函数Ψ的Caputo-Orlicz框架及其图的精确分形维数
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-25 DOI: 10.1016/j.chaos.2026.118148
R.G.P. Sudha, R. Uthayakumar
Fractional calculus provides a fundamental analytical framework for modeling nonlocal and memory-dependent phenomena in complex and biological systems, where classical smoothness assumptions often fail. In this paper, we develop a unified Caputo–Orlicz framework for the geometric analysis of continuous functions whose Caputo fractional derivatives possess bounded Ψ-variation, with Ψ a superlinear Young function. Using Orlicz–Hölder inequalities and Luxemburg norm techniques, we prove that the Caputo fractional derivative acts as a bounded linear operator on Orlicz variation spaces and preserves controlled modulus of continuity properties. These analytic results enable us to derive sharp bounds and exact formulas for the Hausdorff and box-counting dimensions of function graphs over both smooth and possibly fractal domains. In particular, we show that superlinear Orlicz growth enforces minimal graph dimensionality, revealing a sharp transition between smooth and fractal geometric regimes. This work establishes a rigorous connection between fractional differentiation, generalized variation theory, and fractal geometry, providing a flexible theoretical foundation for analyzing nonlinear fractional models that arise in contemporary applied mathematics.
分数阶微积分为复杂系统和生物系统中的非局部和记忆依赖现象建模提供了一个基本的分析框架,在这些系统中,经典的平滑假设常常失败。本文建立了一个统一的Caputo - orlicz框架,用于Caputo分数阶导数具有有界Ψ-variation的连续函数的几何分析,其中Ψ是一个超线性Young函数。利用Orlicz-Hölder不等式和Luxemburg范数技术,证明了Caputo分数阶导数在Orlicz变分空间上是一个有界线性算子,并保持了连续性质的可控模。这些分析结果使我们能够推导出函数图在光滑域和可能的分形域上的Hausdorff维数和盒计数维数的明确界限和精确公式。特别地,我们证明了超线性Orlicz增长强制最小化图维数,揭示了平滑和分形几何制度之间的急剧过渡。本文在分数阶微分、广义变分理论和分形几何之间建立了严密的联系,为分析当代应用数学中出现的非线性分数阶模型提供了灵活的理论基础。
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引用次数: 0
From Hertzian contact to Pochhammer-Chree dynamics: Solitons, chaos, and bifurcation in granular metamaterials 从赫兹接触到波查哈默-克里动力学:粒状超材料中的孤子、混沌和分岔
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-26 DOI: 10.1016/j.chaos.2026.118133
Mst. Ifat Zahan Soma , Tarikul Islam , Tobibur Rahman , Shahariar Ryehan
This study is concerned with the complex propagation patterns of solitary waves within one-dimensional metamaterials consisting of discrete granular elements. Granular mechanics relies heavily on the Hertzian contact theory, a concept which has not been adequately captured by linearised models of particulate contact. In this work, the Hertz theory of contacts is extended to the nonlinear Pochhammer-Chree equation, incorporating spatiotemporal dispersion effects. We present exact solitary wave solutions using the improved auxiliary equation and the improved tan-hyperbolic methods. These methods provide solutions which include the Kink, Anti-kink, Dipole, and Bell-shaped solitary waves, as well as compactons, which have characteristic localisation of energy. The progression of these wave patterns with differing roughness parameters is depicted through three-dimensional surface plots and contour profiles. A comprehensive bifurcation analysis has been carried out to establish the system's stability and to examine the onset of chaos, which is induced by external forcing, by applying the Melnikov theory. Analytical predictions are validated against Discrete Element Method (DEM) simulations, demonstrating excellent agreement with an Error Value (RMSE) of approximately 1.2%. The computed Lyapunov exponent was positive (1.9515), which suggests that the system is sensitive to initial conditions. This new approach is the most advanced that has been developed to date for calculating the nonlinear propagation of stress waves and is essential for designing materials and structures that are resistant to earthquake damage.
本文研究了孤立波在由离散颗粒元组成的一维超材料中的复杂传播模式。颗粒力学在很大程度上依赖于赫兹接触理论,这个概念还没有被颗粒接触的线性化模型充分捕获。在这项工作中,赫兹接触理论被扩展到非线性Pochhammer-Chree方程,并纳入了时空色散效应。利用改进的辅助方程和改进的tan-双曲方法,给出了孤立波的精确解。这些方法提供的解决方案包括扭结、反扭结、偶极子和钟形孤立波,以及具有能量局域化特征的紧子。通过三维表面图和等高线来描述这些具有不同粗糙度参数的波浪模式的进展。应用Melnikov理论对系统进行了全面的分岔分析,建立了系统的稳定性,并检验了由外力引起的混沌的开始。根据离散元法(DEM)模拟验证了分析预测,结果显示误差值(RMSE)约为1.2%。计算得到的Lyapunov指数为正(1.9515),表明系统对初始条件敏感。这种新方法是迄今为止最先进的计算应力波非线性传播的方法,对于设计抗地震破坏的材料和结构至关重要。
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引用次数: 0
Infinite emergent oscillations with locally stable equilibrium 具有局部稳定平衡的无限涌现振荡
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-17 DOI: 10.1016/j.chaos.2026.118090
Ning Wang , Bei Gao , Haoming Zou , Wentao Liu , Zhixuan Ma , Herbert Ho-Ching Iu , Quan Xu
The emergence of multistable states brings about significant unpredictability and complexity in nonlinear dynamical systems, which will induce undesired states and may lead to critical failures or misleading dynamics detection. In this paper, a simple five-term autonomous dissipative chaotic system with unique sine nonlinearity is presented. Notably, an infinite many coexisting attractors can emerge even if the system has a single Lyapunov and Jacobi stable equilibrium point. These attractors cannot be triggered by the initial trajectories near the small neighborhoods of the stable equilibrium point, leading to hidden extreme multistability. Bifurcation route, phase portraits, and basin of attraction confirm coexistence among different periodic and chaotic hidden oscillations. To reveal the boundary between the hidden oscillations and the locally stable space, Jacobi stability and instable boundary analysis using Kosambi–Cartan–Chern theory based on the principles of Finsler space theory are presented. Besides, a predefined-time controller is designed to stabilize the hidden oscillations, which has highlights in the independence between the initial conditions and the predefined settling time, as well as a single flexible adjusted parameter. Simulation experiments confirm the correctness of the theoretical analyses.
多稳定状态的出现给非线性动力系统带来了极大的不可预测性和复杂性,这将诱发非期望状态,并可能导致临界故障或误导动力学检测。本文给出了一个具有唯一正弦非线性的简单五项自治耗散混沌系统。值得注意的是,即使系统只有一个Lyapunov和Jacobi稳定平衡点,也可以出现无限多个共存吸引子。这些吸引子不能被稳定平衡点小邻域附近的初始轨迹触发,从而导致隐藏的极端多重稳定性。分岔路径、相图和引力盆地证实了不同周期混沌隐振荡之间的共存。为了揭示隐振荡与局部稳定空间之间的边界,在Finsler空间理论的基础上,利用kosambii - cartan - chern理论进行了Jacobi稳定性和不稳定边界分析。此外,设计了一个预定义时间控制器来稳定隐藏振荡,其突出特点是初始条件与预定义的稳定时间之间的独立性,以及单一的柔性可调参数。仿真实验验证了理论分析的正确性。
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引用次数: 0
Decision complexity in co-opetitive supply chain: Innovation spillover under cartel and non-cooperative modes 合作竞争供应链中的决策复杂性:卡特尔与非合作模式下的创新溢出
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-16 DOI: 10.1016/j.chaos.2026.118055
Yuanyuan Zhang, Shaochuan Fu, Zihan Ma, Fangfang Ma
Sourcing from competitors triggers innovation spillovers that challenge cooperative stability and strategic decisions. This study employs a nonlinear dynamic game-theoretic model to analyze supply chain behavior under two innovation modes: non-cooperative (firms independently set prices and innovation levels) and cartel cooperative (joint innovation optimization followed by independent pricing). Incorporating behavioral economics (perceived unfairness) and market heterogeneity (brand differentiation), the model reveals how strategic interactions drive system evolution. Key findings demonstrate that while high innovation spillovers enhance knowledge sharing and increase cartel profits within stable regimes, they simultaneously amplify system fragility—exceeding critical spillover thresholds induces bifurcation and chaotic dynamics, disrupting pricing mechanisms and causing severe profit volatility. Furthermore, perceived unfairness reduces cooperation willingness through negative feedback loops, destabilizing alliances, while brand differentiation exhibits dual effects: moderate levels bolster market stability whereas excessive differentiation erodes resilience. Attraction basin analysis confirms the coexistence of multi-stability states (periodic, quasi-periodic, chaotic), highlighting strategic uncertainty.
从竞争对手那里采购会引发创新溢出效应,挑战合作的稳定性和战略决策。本文采用非线性动态博弈论模型分析了两种创新模式下的供应链行为:非合作模式(企业自主设定价格和创新水平)和卡特尔合作模式(联合创新优化后自主定价)。该模型结合了行为经济学(感知不公平)和市场异质性(品牌差异化),揭示了战略互动如何驱动系统进化。主要研究结果表明,虽然在稳定的制度下,高创新溢出可以促进知识共享并增加卡特尔利润,但它们同时也放大了系统的脆弱性——超过关键溢出阈值会导致分岔和混乱动态,扰乱定价机制并导致严重的利润波动。此外,感知不公平通过负反馈循环降低合作意愿,破坏联盟的稳定,而品牌差异化表现出双重效应:适度的差异化增强了市场稳定性,而过度的差异化则削弱了弹性。吸引力盆地分析证实了多稳定状态(周期性、准周期性、混沌)的共存,突出了战略不确定性。
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引用次数: 0
Nonlinear response identification of a parametrically excited bistable magnetic rolling pendulum harvester by 0–1 test and recurrence plots 用0-1试验和递归图识别参数激励双稳态磁摆收割机的非线性响应
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-20 DOI: 10.1016/j.chaos.2026.118077
Wei Wang , Zihao Yang , Enna Zhang , Shuangyan Liu , Xiaoqing Ma , Zilin Li , Ronghan Wei
Owing to the low damping characteristics, magnetic rolling pendulum gains extensive adoption in vibration energy harvesting. Bistable magnetic rolling pendulum harvester (BMRPH) exhibits chaotic and (quasi-)periodic vibrational responses, and effectively identifying the complex dynamic behaviors is essential for advancing practical applications. Therefore, this paper utilizes 0–1 test and recurrence plot (RP) to examine the nonlinear voltage response time series of a parametrically excited BMRPH. By analyzing the nonlinear dynamics of the BMRPH, multiple vibrational patterns are emphasized. Results indicate that 0–1 test could easily distinguish between chaotic and periodic responses through the trajectory plot of (p, q), total mean square displacement, and asymptotic growth rate. Unlike 0–1 test, which provides a binary classification (0 for periodic and 1 for chaotic systems), RP offers a more nuanced approach by not only distinguishing between chaotic and periodic dynamics but also revealing the relative complexity within periodic regimes. In general, the identification results align well with complementary diagnostic methods, including phase portraits, Poincaré maps, frequency spectra, and multiscale entropy, thereby offering valuable insights for optimizing the dynamic performance and enhancing energy harvesting efficiency.
由于低阻尼特性,磁摆在振动能量收集中得到了广泛的应用。双稳态磁摇摆收割机(BMRPH)表现出混沌和(准)周期的振动响应,有效识别其复杂的动力学行为对于推进实际应用至关重要。因此,本文利用0-1试验和递归图(RP)来检验参数激励BMRPH的非线性电压响应时间序列。通过分析BMRPH的非线性动力学,强调了其多种振动模式。结果表明,通过(p, q)、总均方位移和渐近增长率的轨迹图,0-1检验可以很容易地区分混沌响应和周期响应。与0 - 1测试不同,它提供了一个二元分类(0为周期系统,1为混沌系统),RP提供了一个更细致的方法,不仅区分了混沌和周期动力学,而且揭示了周期制度内的相对复杂性。总体而言,识别结果与相位肖像、庞加莱图、频谱和多尺度熵等互补诊断方法一致,从而为优化动态性能和提高能量收集效率提供了有价值的见解。
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引用次数: 0
Boundary-induced multistability and bursting oscillations in frequency switching slow–fast systems 频率开关慢快系统的边界诱导多稳定性和突发振荡
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-19 DOI: 10.1016/j.chaos.2026.118080
Jiahao Zhao , Xiujing Han , Wenjie Zuo , Jiadong Wang , Meng Han
Frequency-switching mechanisms, prevalent in engineering and scientific dynamical systems, introduce non-smooth dynamics that significantly impact system behavior. This study integrates frequency switching with slow–fast analysis in non-smooth dynamical systems, emphasizing the role of switching-induced multistability in shaping bursting dynamics. Using a modified normal-form vector field of a transcritical bifurcation subjected to state-dependent frequency-switching excitation, we show that although individual subsystems exhibit only equilibrium solutions, their interactions across the switching boundary induce non-smooth periodic orbits. These limit cycles coexist with equilibria, yielding switching-induced multistability. This multistability governs frequency-switching dynamics and determines the organization, patterns, and stability of bursting oscillations through a dual regulation mechanism involving the switching threshold and initial conditions: the switching threshold drives bifurcation evolution to control post-switching attractor selection, yielding diverse bursting patterns characterized by monostable–monostable, bistable–bistable, and bistable–monostable switching sequences; meanwhile, initial conditions exploit multistability to provide alternative stable switching pathways, thereby avoiding trajectory divergence during switching transitions and stabilizing bursting solutions. Our findings contribute to the characterizing and regulating bursting dynamics in frequency-switching systems.
频率开关机制,普遍存在于工程和科学动力系统中,引入非光滑动力学,显著影响系统行为。本研究将非光滑动力系统的频率开关与慢速分析相结合,强调开关诱导的多稳定性在形成爆破动力学中的作用。利用受状态相关的频率开关激励的跨临界分岔的修正范式向量场,我们证明了尽管单个子系统仅表现出平衡解,但它们在开关边界上的相互作用诱导出非光滑的周期轨道。这些极限环与平衡点共存,产生切换诱导的多稳定性。这种多稳定性控制着频率切换动力学,并通过涉及开关阈值和初始条件的双重调节机制决定了爆发振荡的组织、模式和稳定性:开关阈值驱动分岔进化以控制开关后吸引子的选择,产生以单稳定-单稳定、双稳定-双稳定和双稳定-单稳定开关序列为特征的多种爆发模式;同时,初始条件利用多稳定性提供了可选的稳定切换路径,从而避免了切换过渡过程中的轨迹发散,稳定了突发解。我们的发现有助于表征和调节频率开关系统的爆破动力学。
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引用次数: 0
Robustness of interdependent directed hypergraphs with completely connected component 具有完全连通分量的相互有向超图的鲁棒性
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-21 DOI: 10.1016/j.chaos.2026.118091
Zhengao Guo , Yinzuo Zhou , Jie Zhou
Directed hypergraphs (DH) provide a powerful framework for characterizing directional influences and higher-order interactions in complex systems. In many real-world systems, the group interactions represented by directed hyperedges generally have an inherent requirement of integrity, meaning their functionality depends on the simultaneous presence of all participating nodes. Traditional definition of strongly connected components that was proposed for classic directed graphs do not explicitly capture this requirement, which may lead to biased evaluation in the robustness of the system. To address this issue, we introduce the concept of the Completely Connected Component (CCC) of DH as a pertinent representation for such connectivity. By requiring that every directed hyperedge should satisfy the integrity condition, the CCC ensures the preservation of nodes incident to related hyperedges. In this paper we study the robustness of interdependent DH from the perspective of CCC, which has wide applications in many real-world systems. Based on a bipartite representation of DH, we develop a theoretical framework for analyzing the system. We systematically evaluate the system’s robustness under different types of interdependencies induced from CCC. Our analysis shows that the requirement of the integrity of hyperedges will markedly influence the robustness of the system, which is verified with numerical simulations. Specifically, since the CCC condition reinforces the preservation of nodes, interdependence between hypergraphs that takes place on nodes typically exhibit stronger robustness than that involving hyperedges. However, the system could be more vulnerable when the initial damage targets nodes rather than hyperedges. By analyzing the competing effects induced by the CCC on both the initial damage and the objects involved in the interdependence, non-monotonic behaviors of the system robustness are revealed. Our finding offers a deeper understanding of the robustness of systems with high-order interactions across various interdependence scenarios.
有向超图(DH)为描述复杂系统中的定向影响和高阶相互作用提供了一个强大的框架。在许多现实世界的系统中,由有向超边缘表示的组交互通常具有固有的完整性要求,这意味着它们的功能依赖于所有参与节点的同时存在。针对经典有向图提出的传统强连接分量定义没有明确地捕捉到这一要求,这可能导致系统鲁棒性评估的偏差。为了解决这个问题,我们引入了DH的完全连接组件(CCC)的概念,作为这种连接的相关表示。通过要求每个有向超边都满足完整性条件,CCC保证了关联超边上的节点的保留。本文从CCC的角度研究了相互依赖DH的鲁棒性,该方法在许多现实系统中有着广泛的应用。基于DH的二部表示,我们开发了一个分析系统的理论框架。我们系统地评估了系统在CCC引起的不同类型的相互依赖下的鲁棒性。分析表明,超边完整性的要求会显著影响系统的鲁棒性,并通过数值仿真验证了这一点。具体来说,由于CCC条件加强了节点的保存,发生在节点上的超图之间的相互依赖通常比涉及超边的超图表现出更强的鲁棒性。然而,当初始损伤目标是节点而不是超边缘时,系统可能更容易受到攻击。通过分析CCC对初始损伤和相互依赖对象的竞争效应,揭示了系统鲁棒性的非单调行为。我们的发现为跨各种相互依赖场景的高阶交互系统的鲁棒性提供了更深入的理解。
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引用次数: 0
Physical approach to control ion channel in a neuron 控制神经元离子通道的物理方法
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-19 DOI: 10.1016/j.chaos.2026.118079
Jun Ma , Jiarong Zhao , Binchi Wang , Chunni Wang
Blockers and activators can modify the conductance of the ion channels, and the channel currents are changed to regulate the membrane potential of a neuron for presenting different firing patterns. From dynamical aspect, blocking the ion channel and external stimuli are processed by adding equivalent trans-membrane current on the neuron models, however, the physical processing is not clarified. In this article, a control branch shunts channel current from the inductive channel of the FitzHugh-Nagumo (FHN) neural circuit, and external stimuli can be encoded in the ion channel rather than imposing direct forcing currents on the membrane potential. The neural circuit is controlled by shunting current from the inductor of the branch circuit in the FHN neural circuit, a constant voltage connected with a memristor is used to generate forcing current within finite frequency band rather than sole frequency, which is consistent with realistic external stimuli. The control branch circuit composes a capacitor for filtering the external stimulus and the filtered current will interact with the shunted channel current under energy exchange, as a result, changes of the energy ratio between magnetic field and electric field will modify the capacitor voltage, which corresponds to the membrane potential of the neuron model. Energy function is provided to discern the correlation between firing modes and energy level, and then coherence resonance is induced under noisy disturbance. Our results provide new insights into control of ion channels from physical aspect, that is, external energy injection via the control branch circuit (external sub-branch circuit) into the neural circuit tends to build a hybrid ion channel for regulating the energy level of the neurons. As a result, the ion channel becomes controllable following the injection of energy flow and the channel conductance becomes controllable. Therefore, the external energy is encoded in the ion channel for further adjustment in the energy level of the neuron, and then the energy levels control the neural activities.
阻滞剂和激活剂可以改变离子通道的电导,并改变通道电流来调节神经元的膜电位,以呈现不同的放电模式。从动力学角度看,阻断离子通道和外部刺激是通过在神经元模型上加入等效的跨膜电流来处理的,但物理处理尚不清楚。在本文中,一个控制分支从FitzHugh-Nagumo (FHN)神经回路的感应通道分流通道电流,外部刺激可以在离子通道中编码,而不是在膜电位上施加直接强迫电流。该神经回路通过FHN神经回路支路电感的分流电流进行控制,利用恒压与忆阻器连接产生有限频带内的强制电流,而非单一频率,与现实外界刺激相一致。控制支路组成一个滤波外部刺激的电容器,滤波后的电流在能量交换下与分流通道电流相互作用,磁场与电场能量比的变化会改变电容器电压,这与神经元模型的膜电位相对应。利用能量函数识别发射模式与能级之间的关系,在噪声干扰下诱发相干共振。我们的研究结果从物理角度对离子通道的控制提供了新的见解,即通过控制分支电路(外部子分支电路)向神经回路注入外部能量,倾向于建立一个混合离子通道来调节神经元的能量水平。因此,离子通道在注入能量流后变得可控,通道电导变得可控。因此,外部能量被编码到离子通道中,进一步调节神经元的能量水平,然后能量水平控制神经活动。
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引用次数: 0
Evolutionary dynamics of reactive partner strategy in stochastic games 随机对策中反应性伙伴策略的演化动力学
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2026-07-01 Epub Date: 2026-02-23 DOI: 10.1016/j.chaos.2026.118131
Jing Zhang , Yixin Yang , Zhihai Rong , Zhi-Xi Wu
Stochastic games provide an efficient incentive mechanism for the emergence of cooperation by modeling the feedback between environmental states and individual behaviors, where players usually make decisions through memory strategies. In this paper, a mixed memory-one strategy called the reactive partner strategy (REPA) is introduced into stochastic games, which tends to deterministically cooperate with the cooperative co-player and forgive an opponent’s defection with a probability. By analyzing the payoff relationships between pure memory-one strategies and REPA, it is shown that REPA is always a Nash equilibrium strategy that can resist invasion by defective strategies, and the proper forgiving probability of REPA can promote cooperation under low benefit conditions in stochastic games where the famous pure memory-one strategy of win-stay, lose-shift (WSLS) fails to oppose invasion by defectors. For high benefit values, REPA can act as an evolutionary bridge that connects always defect (AllD), Grim and WSLS strategies, which may offer valuable insights into understanding and promoting both cooperation and strategic evolution in stochastic games.
随机博弈通过模拟环境状态和个体行为之间的反馈,为合作的出现提供了有效的激励机制,玩家通常通过记忆策略做出决策。本文在随机博弈中引入了一种混合记忆-一策略,即反应性伙伴策略(REPA),该策略倾向于确定性地与合作伙伴合作,并有概率地原谅对手的背叛。通过分析纯记忆一策略与REPA之间的收益关系,发现REPA始终是一种能够抵抗缺陷策略入侵的纳什均衡策略,在著名的纯记忆一策略“赢-留-丢-换”(WSLS)无法抵抗叛逃者入侵的随机博弈中,适当的REPA原谅概率能够促进低收益条件下的合作。对于高收益值,REPA可以作为连接总缺陷(AllD)、Grim和WSLS策略的进化桥梁,为理解和促进随机博弈中的合作和策略进化提供有价值的见解。
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引用次数: 0
期刊
Chaos Solitons & Fractals
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