IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0232563

Haitao Li, Lixin Ji, Kai Wang, Shuo Liu, Shuxin Liu

{"title":"Applying the Stackelberg game to assess critical infrastructure vulnerability: Based on a general multi-layer network model.","authors":"Haitao Li, Lixin Ji, Kai Wang, Shuo Liu, Shuxin Liu","doi":"10.1063/5.0232563","DOIUrl":"https://doi.org/10.1063/5.0232563","url":null,"abstract":"Critical infrastructure systems (CIS) are closely related to human life. Attacks against CIS occur frequently, making accurate and effective protection of CIS essential. Vulnerability assessment is the primary issue to achieving this goal. The interconnected characteristic of CIS means that it is best represented by a multi-layer network, but a uniform model is absent. Game theory offers a suitable framework for researching intelligent confrontation. Previous research combining game theory and network science mainly focuses on a single-layer network and lacks a comprehensive assessment that combines qualitative and quantitative aspects of vulnerability. In this paper, we apply the Stackelberg game to the multi-layer network and comprehensively assess vulnerability based on game equilibrium to realize accurate protection. We first present a method for constructing a general model of the multi-layer network and introduce a multi-layer weighted factor to extend topological attribute metrics. Then, we design a Stackelberg game model for the multi-layer network. Furthermore, we qualitatively analyze the impact of multi-layer network characteristics on vulnerability and propose a method to quantify vulnerability. Experiments show that the vulnerability of the multi-layer network is greatly influenced by the multi-layer weighted factor, single-layer network type, and inter-layer coupling method. The quantitative value of network vulnerability does not rely entirely on the topology attributes on which the attack and defense costs depend but also relates to the resources available. Our work provides an adaptive model for CIS and gives a new approach to developing accurate protection based on comprehensive vulnerability assessment, which deserves further study.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142784297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Zero-determinant strategy for distributed state estimation against eavesdropping attacks. 针对窃听攻击的分布式状态估计零行列式策略。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0235693

Yan Yu, Wen Yang, Jialing Chen

{"title":"Zero-determinant strategy for distributed state estimation against eavesdropping attacks.","authors":"Yan Yu, Wen Yang, Jialing Chen","doi":"10.1063/5.0235693","DOIUrl":"https://doi.org/10.1063/5.0235693","url":null,"abstract":"In distributed networks, the transmission of state estimates via wireless channels between neighbor nodes is susceptible to interception by eavesdroppers, leading to significant risks to data privacy. Given the substantial energy and bandwidth consumption of data encryption, sensors with limited energy must strategically decide when to encrypt data. Simultaneously, eavesdroppers with similar energy constraints must determine when to intercept transmissions. In this paper, we propose a game-theoretic approach to this security dilemma and introduce a defense strategy based on zero-determinant (ZD) policies. Initially, we model the interaction between sensors and malicious eavesdroppers in the distributed state estimation as an iterative game. Subsequently, we apply ZD strategies to protect both channel and node data, respectively. We further explore how, under these strategies, sensors can unilaterally set the expected payoff of eavesdroppers or coerce a positive correlation with the expected payoff of sensors. Moreover, we analyze how sensors can devise optimal strategies by maximizing their own utility while minimizing that of the opponent, regardless of the actions of the opponent. The feasibility and effectiveness of the proposed methods are validated through numerical simulations.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mechanism of transition from subdiffusive transport to normal diffusion for passive tracers in a plane periodical flow induced by Gaussian noise. 高斯噪声诱导的平面周期性流动中被动示踪剂由亚扩散输运向正扩散转变的机理。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0224277

Boris S Maryshev, Lyudmila S Klimenko

{"title":"Mechanism of transition from subdiffusive transport to normal diffusion for passive tracers in a plane periodical flow induced by Gaussian noise.","authors":"Boris S Maryshev, Lyudmila S Klimenko","doi":"10.1063/5.0224277","DOIUrl":"https://doi.org/10.1063/5.0224277","url":null,"abstract":"The known analytical solution describing a two-dimensional viscous flow with vortices under a driving force is generalized. It is shown that a periodic pattern of asymmetric vortices arises when the force amplitude exceeds a critical value. The transport of an ensemble of passive particles through the resulting structure has been studied. The envelope of each vortex contains a stagnation point, and the tracer motion along it without noise is infinitely long. It is shown that the macroscopic transport of an ensemble of tracers is extremely slow in the noise-free case. The latter leads to the mixing of the tracer ensemble. We study the peculiarities of such transport using a special flow model. Such a model has the form of a series of recurrence mappings. The recurrence mappings are constructed for the ensemble transport through a unit cell using the numerical solution of the Langevin equations in the presence of random particle displacements caused by molecular diffusion. The presence of diffusion allows particles to penetrate into the vortex, which leads to an additional slowing down of transport. The effect of noise on the variance of the tracer ensemble is investigated. It is shown that the growth of the standard deviation with time can be described by a power law. On an intermediate time scale, which grows exponentially long, as the noise strength tends to zero, a subdiffusive behavior is observed. The dependence of the subdiffusion exponent on the molecular diffusivity is obtained.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Regime switching in coupled nonlinear systems: Sources, prediction, and control-Minireview and perspective on the Focus Issue. 耦合非线性系统中的状态切换：来源、预测和控制——对焦点问题的回顾和展望。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0247498

Igor Franović, Sebastian Eydam, Deniz Eroglu

{"title":"Regime switching in coupled nonlinear systems: Sources, prediction, and control-Minireview and perspective on the Focus Issue.","authors":"Igor Franović, Sebastian Eydam, Deniz Eroglu","doi":"10.1063/5.0247498","DOIUrl":"https://doi.org/10.1063/5.0247498","url":null,"abstract":"Regime switching, the process where complex systems undergo transitions between qualitatively different dynamical states due to changes in their conditions, is a widespread phenomenon, from climate and ocean circulation, to ecosystems, power grids, and the brain. Capturing the mechanisms that give rise to isolated or sequential switching dynamics, as well as developing generic and robust methods for forecasting, detecting, and controlling them is essential for maintaining optimal performance and preventing dysfunctions or even collapses in complex systems. This Focus Issue provides new insights into regime switching, covering the recent advances in theoretical analysis harnessing the reduction approaches, as well as data-driven detection methods and non-feedback control strategies. Some of the key challenges addressed include the development of reduction techniques for coupled stochastic and adaptive systems, the influence of multiple timescale dynamics on chaotic structures and cyclic patterns in forced systems, and the role of chaotic saddles and heteroclinic cycles in pattern switching in coupled oscillators. The contributions further highlight deep learning applications for predicting power grid failures, the use of blinking networks to enhance synchronization, creating adaptive strategies to control epidemic spreading, and non-feedback control strategies to suppress epileptic seizures. These developments are intended to catalyze further dialog between the different branches of complexity.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamical modeling and analysis of epileptic discharges transition caused by glutamate release with metabolism processes regulation from astrocyte. 星形胶质细胞代谢过程调控谷氨酸释放引起癫痫放电转变的动力学建模与分析。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0236770

Duo Li, Qiang Li, Rui Zhang

{"title":"Dynamical modeling and analysis of epileptic discharges transition caused by glutamate release with metabolism processes regulation from astrocyte.","authors":"Duo Li, Qiang Li, Rui Zhang","doi":"10.1063/5.0236770","DOIUrl":"https://doi.org/10.1063/5.0236770","url":null,"abstract":"Glutamate (Glu) is a crucial excitatory neurotransmitter in the central nervous system that transmits brain information by activating excitatory receptors on neuronal membranes. Physiological studies have demonstrated that abnormal Glu metabolism in astrocytes is closely related to the pathogenesis of epilepsy. The astrocyte metabolism processes mainly involve the Glu uptake through astrocyte EAAT2, the Glu-glutamine (Gln) conversion, and the Glu release. However, the relationship between these Glu metabolism processes and epileptic discharges remains unclear. In this paper, we propose a novel neuron-astrocyte model by integrating the dynamical modeling of astrocyte Glu metabolism processes, which include Glu metabolism in astrocytes consisting of the Glu uptake, Glu-Gln conversion, Glu diffusion, and the resulting Glu release as well as Glu-mediated bidirectional communication between neuron and astrocyte. Furthermore, the influences of astrocyte multiple Glu metabolism processes on the Glu release and dynamics transition of neuronal epileptic discharges are verified through numerical experiments and dynamical analyses from various nonlinear dynamics perspectives, such as time series, phase plane trajectories, interspike intervals, and bifurcation diagrams. Our results suggest that the downregulation expression of EAAT2 uptake, the slowdown of the Glu-Gln conversion rate, and excessively elevated Glu equilibrium concentration in astrocytes can cause an increase in Glu released from astrocytes, which results in the aggravation of epileptic seizures. Meanwhile, neuronal epileptic discharge states transition from bursting to mixed-mode spiking and tonic firing induced by the combination of these abnormal metabolism processes. This study provides a theoretical foundation and dynamical analysis methodology for further exploring the dynamics evolution and physiopathological mechanisms of epilepsy.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142881338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

How neural networks work: Unraveling the mystery of randomized neural networks for functions and chaotic dynamical systems. 神经网络如何工作：解开函数和混沌动力系统的随机神经网络之谜。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0206840

Erik Bollt

{"title":"How neural networks work: Unraveling the mystery of randomized neural networks for functions and chaotic dynamical systems.","authors":"Erik Bollt","doi":"10.1063/5.0206840","DOIUrl":"https://doi.org/10.1063/5.0206840","url":null,"abstract":"Artificial Neural Networks (ANNs) have proven to be fantastic at a wide range of machine learning tasks, and they have certainly come into their own in all sorts of technologies that are widely consumed today in society as a whole. A basic task of machine learning that neural networks are well suited to is supervised learning, including when learning orbits from time samples of dynamical systems. The usual construct in ANN is to fully train all of the perhaps many millions of parameters that define the network architecture. However, there are certain ANN algorithms that work well with random designs. We have previously presented an explanation as to how the reservoir computing recurrent neural network architecture succeeds despite randomness. Here, we explain how the random feedforward neural networks called the random project networks work. In particular, we present examples for both general function learning and also for learning a flow from samples of orbits of chaotic dynamical systems. There is an interesting geometric explanation of the success, in the case of the ReLu activation function, that relates to the classical mathematical question of how configurations of random lines fall in a plane, or how planes or hyperplanes may fall in higher dimensional spaces. These random configurations lead to a refinement of the domain so that piecewise linear continuous functions result that are dense in continuous functions. This relates neural networks to finite element methods. We highlight the universality of this representation by forecasting the skill of chaotic dynamical systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142881344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Magnetic structures in the explicitly time-dependent nontwist map. 显式随时间变化的非扭曲图中的磁结构

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0231530

Dániel Jánosi, Anikó Horváth, Lili Édes, Tamás Kovács

{"title":"Magnetic structures in the explicitly time-dependent nontwist map.","authors":"Dániel Jánosi, Anikó Horváth, Lili Édes, Tamás Kovács","doi":"10.1063/5.0231530","DOIUrl":"https://doi.org/10.1063/5.0231530","url":null,"abstract":"We investigate how the magnetic structures of the plasma change in a large aspect ratio tokamak perturbed by an ergodic magnetic limiter, when a system parameter is non-adiabatically varied in time. We model such a scenario by considering the Ullmann-Caldas nontwist map, where we introduce an explicit time-dependence to the ratio of the limiter and plasma currents. We apply the tools developed recently in the field of chaotic Hamiltonian systems subjected to parameter drift. Namely, we follow trajectory ensembles initially forming Kolmogorov Arnold Moser (KAM) tori and island chains in the autonomous configuration space. With a varying parameter, these ensembles, called snapshot tori, develop time-dependent shapes. An analysis of the time evolution of the average distance of point pairs in such an ensemble reveals that snapshot tori go through a transition to chaos, with a positive Lyapunov exponent. We find empirical power-law relationships between both the Lyapunov exponent and the beginning of the transition to chaos (the so-called critical instant), as a function of the rate of the parameter drift, with the former showing an increasing trend and the latter a decreasing trend. We conclude that, in general, coherent tori and magnetic islands tend to break up and become chaotic as the perturbation increases, similar to the case of subsequent constant perturbations. However, because of the continuous drift, some structures can persist longer and exist even at perturbation values where they would not be observable in the constant perturbation case.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142863495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Periodic external driving of transmission-delay-coupled phase oscillator system: Switching between different twisted states. 传输延迟耦合相振系统的周期性外部驱动：不同扭态之间的切换。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0214720

Jin-Song Kang, Yong-Hyok An, Ryong-Son Kim, Chol-Ung Choe

{"title":"Periodic external driving of transmission-delay-coupled phase oscillator system: Switching between different twisted states.","authors":"Jin-Song Kang, Yong-Hyok An, Ryong-Son Kim, Chol-Ung Choe","doi":"10.1063/5.0214720","DOIUrl":"https://doi.org/10.1063/5.0214720","url":null,"abstract":"We consider the effects of an external periodic forcing on a spatially extended system that consists of identical phase oscillators coupled with transmission delays on a ring. Analyzing the continuum limit N→∞ of the model system along the Ott-Antonsen invariant manifold, we obtain the stability diagram for two regimes, called the forced and drifting entrainments. The former exhibits a spatially homogeneous solution trying to lock onto the drive, of which the stability boundary is rigorously determined. The latter represents a spatially organized group of oscillators that entrain one another at a frequency different from that of the drive. We show that in the drifting entrainment the external driving triggers the occurrence of unusual twisted states, characterized by nonuniform phase gradient as well as by the traveling wave of the order parameter amplitude. Moreover, it is found that by increasing or decreasing the forcing strength one can effectively switch between twisted states with different winding numbers. Our theoretical and numerical results for the reduced system are supported by the direct numerical simulations of the model system.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A dynamical study of Hilda asteroids in the Circular and Elliptic RTBP. 希尔达小行星在圆形和椭圆形RTBP中的动力学研究。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0234410

Àngel Jorba, Begoña Nicolás, Óscar Rodríguez

引用次数: 0

Synchronization cluster bursting in adaptive oscillator networks. 自适应振荡网络中的同步簇爆发。

IF 2.7 2区数学

Chaos Pub Date : 2024-12-01 DOI: 10.1063/5.0226257

Mengke Wei, Andreas Amann, Oleksandr Burylko, Xiujing Han, Serhiy Yanchuk, Jürgen Kurths

引用次数: 0

Chaos最新文献