Pub Date : 2024-10-23DOI: 10.1016/j.chaos.2024.115650
Firoz Chogle , Seba Sara Varghese , Abdel-Baset M.A. Ibrahim , Awadhesh Prasad , Hichem Eleuch
This paper presents a study of the dynamical behavior in a cavity-assisted two-channel Kerr nonlinear directional coupler. Applying a deterministic periodic laser pump to a two-channel coupled system led to a range of dynamic behaviors, encompassing periodicity, quasiperiodicity, chaoticity and hyperchaoticity. This is confirmed by the exploration of the Lyapunov exponents, Poincaré sections and bifurcation diagrams for resonance and low cavity detuning. For low cavity detuning, chaos arises when the laser pump’s amplitude is large. This is due to higher interactions between photons and the cavity, resulting in more photons inside and higher nonlinearity. On the other hand, the reduced interactions in high cavity detuning displayed regular behavior which is explained qualitatively.
{"title":"Chaos and regularities in cavity assisted two-channel nonlinear coupler","authors":"Firoz Chogle , Seba Sara Varghese , Abdel-Baset M.A. Ibrahim , Awadhesh Prasad , Hichem Eleuch","doi":"10.1016/j.chaos.2024.115650","DOIUrl":"10.1016/j.chaos.2024.115650","url":null,"abstract":"<div><div>This paper presents a study of the dynamical behavior in a cavity-assisted two-channel Kerr nonlinear directional coupler. Applying a deterministic periodic laser pump to a two-channel coupled system led to a range of dynamic behaviors, encompassing periodicity, quasiperiodicity, chaoticity and hyperchaoticity. This is confirmed by the exploration of the Lyapunov exponents, Poincaré sections and bifurcation diagrams for resonance and low cavity detuning. For low cavity detuning, chaos arises when the laser pump’s amplitude is large. This is due to higher interactions between photons and the cavity, resulting in more photons inside and higher nonlinearity. On the other hand, the reduced interactions in high cavity detuning displayed regular behavior which is explained qualitatively.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115650"},"PeriodicalIF":5.3,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.chaos.2024.115662
Zhe Li, Jin Liu, Jiaqi Ren, Yibo Dong, Weili Li
Critical infrastructure networks serve as the backbone of modern society’s operations, and the application of game theory to safeguard these networks against deliberate attacks under resource constraints is of paramount importance. Regrettably, the existing body of research on hybrid attack and defense strategies for nodes and edges is notably scarce, despite the ubiquity of such strategies in practical contexts. Current understanding regarding the establishment of a cost constraint model within the framework of hybrid attack and defense strategies, the strategic inclinations of both adversarial and defensive parties under varying cost constraint coefficients, and the influence of resource allocation ratios on equilibrium outcomes remains limited. Consequently, this study constructs a game-theoretic model for the engagement of critical infrastructure networks under non-uniform cost constraints, incorporating hybrid attack and defense strategies for nodes and edges, and conducts an equilibrium analysis across a range of cost constraint coefficients and resource allocation ratios. The findings reveal that when resource availability is limited, both attackers and defenders are inclined towards a strategy of concentrated resource allocation; in contrast, under most circumstances, defenders exhibit a preference for an equitable distribution of resources.
{"title":"Application of hybrid strategies of complex network attack and defense games","authors":"Zhe Li, Jin Liu, Jiaqi Ren, Yibo Dong, Weili Li","doi":"10.1016/j.chaos.2024.115662","DOIUrl":"10.1016/j.chaos.2024.115662","url":null,"abstract":"<div><div>Critical infrastructure networks serve as the backbone of modern society’s operations, and the application of game theory to safeguard these networks against deliberate attacks under resource constraints is of paramount importance. Regrettably, the existing body of research on hybrid attack and defense strategies for nodes and edges is notably scarce, despite the ubiquity of such strategies in practical contexts. Current understanding regarding the establishment of a cost constraint model within the framework of hybrid attack and defense strategies, the strategic inclinations of both adversarial and defensive parties under varying cost constraint coefficients, and the influence of resource allocation ratios on equilibrium outcomes remains limited. Consequently, this study constructs a game-theoretic model for the engagement of critical infrastructure networks under non-uniform cost constraints, incorporating hybrid attack and defense strategies for nodes and edges, and conducts an equilibrium analysis across a range of cost constraint coefficients and resource allocation ratios. The findings reveal that when resource availability is limited, both attackers and defenders are inclined towards a strategy of concentrated resource allocation; in contrast, under most circumstances, defenders exhibit a preference for an equitable distribution of resources.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115662"},"PeriodicalIF":5.3,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.chaos.2024.115665
Hongwei Kang , Xin Li , Yong Shen, Xingping Sun, Qingyi Chen
In the realm of spatial public goods games, heterogeneous investment has emerged as a potent mechanism to enhance cooperative behavior. Savvy investors dynamically adjust their investment levels to optimize returns based on environmental conditions and personal circumstances. This study delves into the evolution of cooperation within a spatial public goods game framework, characterized by heterogeneous investment and associated risks, conducted on a square lattice. We introduce the investors (I) with heterogeneous investment, who updates his investment amount according to the current environment of the game and his own historical experience. We introduce a particle swarm optimization algorithm with decaying historical returns to fine-tune the investment levels of investors. Furthermore, a risk mechanism inspired by the ultimatum game is integrated into the model. This paper investigates the impact of the risk threshold on cooperative behavior and examines the influence of the risk decay factor on cooperation. Additionally, it analyzes the investment behavior of investors in scenarios where two types of investors coexist. Finally, this study explores the effects of the historical best payoff decay factor and the self-learning rate on cooperative behavior. This research contributes to a nuanced understanding of heterogeneous investment behaviors in public goods games under specified risk mechanisms, providing novel insights into the intricate dynamics of cooperation in complex systems.
{"title":"Particle swarm optimization with historical return decay enhances cooperation in public goods games with investment risks","authors":"Hongwei Kang , Xin Li , Yong Shen, Xingping Sun, Qingyi Chen","doi":"10.1016/j.chaos.2024.115665","DOIUrl":"10.1016/j.chaos.2024.115665","url":null,"abstract":"<div><div>In the realm of spatial public goods games, heterogeneous investment has emerged as a potent mechanism to enhance cooperative behavior. Savvy investors dynamically adjust their investment levels to optimize returns based on environmental conditions and personal circumstances. This study delves into the evolution of cooperation within a spatial public goods game framework, characterized by heterogeneous investment and associated risks, conducted on a square lattice. We introduce the investors (I) with heterogeneous investment, who updates his investment amount according to the current environment of the game and his own historical experience. We introduce a particle swarm optimization algorithm with decaying historical returns to fine-tune the investment levels of investors. Furthermore, a risk mechanism inspired by the ultimatum game is integrated into the model. This paper investigates the impact of the risk threshold <span><math><mi>θ</mi></math></span> on cooperative behavior and examines the influence of the risk decay factor <span><math><mi>α</mi></math></span> on cooperation. Additionally, it analyzes the investment behavior of investors in scenarios where two types of investors coexist. Finally, this study explores the effects of the historical best payoff decay factor <span><math><mi>β</mi></math></span> and the self-learning rate <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> on cooperative behavior. This research contributes to a nuanced understanding of heterogeneous investment behaviors in public goods games under specified risk mechanisms, providing novel insights into the intricate dynamics of cooperation in complex systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115665"},"PeriodicalIF":5.3,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.chaos.2024.115675
Xiaoyu Zhu , Rongxia Hao
Identifying influential nodes in social networks has significant applications in terms of social analysis and information dissemination. How to capture the crucial features of influential nodes without increasing the computational complexity is an urgent issue to be solved in the context of big data. Laplacian centrality (LC) measures nodal influence by computing nodes' degree, making it extremely low complexity. However, there is still significant room for improvement. Consequently, we propose the improved Laplacian centrality (ILC) to identify influential nodes based on the concept of self-consistent. Identifying results on 9 real networks prove that ILC is superior to LC and other 6 classical measures in terms of ranking accuracy, top-k nodes identification and discrimination capability. Moreover, the computational complexity of ILC has not significantly increased compared to LC, and remains the linear order of magnitude O(m). Additionally, ILC has excellent robustness and universality such that there is no need to adjust parameters according to different network structures.
{"title":"Identifying influential nodes in social networks via improved Laplacian centrality","authors":"Xiaoyu Zhu , Rongxia Hao","doi":"10.1016/j.chaos.2024.115675","DOIUrl":"10.1016/j.chaos.2024.115675","url":null,"abstract":"<div><div>Identifying influential nodes in social networks has significant applications in terms of social analysis and information dissemination. How to capture the crucial features of influential nodes without increasing the computational complexity is an urgent issue to be solved in the context of big data. Laplacian centrality (LC) measures nodal influence by computing nodes' degree, making it extremely low complexity. However, there is still significant room for improvement. Consequently, we propose the improved Laplacian centrality (ILC) to identify influential nodes based on the concept of self-consistent. Identifying results on 9 real networks prove that ILC is superior to LC and other 6 classical measures in terms of ranking accuracy, top-k nodes identification and discrimination capability. Moreover, the computational complexity of ILC has not significantly increased compared to LC, and remains the linear order of magnitude O(m). Additionally, ILC has excellent robustness and universality such that there is no need to adjust parameters according to different network structures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115675"},"PeriodicalIF":5.3,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.chaos.2024.115647
Soma Bhattacharya, Ebha Koley, Subhojit Ghosh
The integration of high-speed communication networks and synchrophasors into smart grids has significantly improved real-time monitoring and control accuracy. However, the increased reliance on communication infrastructure has also heightened the vulnerability of the power networks to cyber intrusions. Synchronized phasor data and GPS time-stamping used by Phasor Measurement Units (PMUs), make them prime targets for cyber intrusions. Among the different types of intrusions in smart grids, Time Synchronization Attacks (TSA), because of their impact and easier execution, are widely employed by intruders to disrupt grid operations. Such attacks aim at spoofing GPS signals, thereby altering voltage and current phasor information across the network. The same leads to malfunction of the operations executed at the control center. The present work aims to develop a secured and resilient mechanism against TSAs in smart grids. In this regard, a two-stage mechanism based on deep learning and spline interpolation is proposed. The first stage employs an LSTM-based classifier to detect TSAs in the cyber layer. Post-TSA detection, the second stage uses spline interpolation to filter out malicious data. The filtering allows for the restoration of the actual pre-TSA data acquired from PMUs. The proposed TSA detection and correction scheme has been validated extensively across various TSA scenarios on IEEE 9, 14, and 57 bus systems. Majority of the reported works of TSA detection have been validated using offline numerical simulations, which have limitations in replicating practical TSA dynamics. To address the same, the proposed scheme has been validated using a real-time testbed comprising of a digital simulator, real PMU, GPS receiver, and a data acquisition module with a communication interface.
{"title":"Improving resilience of cyber physical power networks against Time Synchronization Attacks (TSAs) using deep learning and spline interpolation with real-time validation","authors":"Soma Bhattacharya, Ebha Koley, Subhojit Ghosh","doi":"10.1016/j.chaos.2024.115647","DOIUrl":"10.1016/j.chaos.2024.115647","url":null,"abstract":"<div><div>The integration of high-speed communication networks and synchrophasors into smart grids has significantly improved real-time monitoring and control accuracy. However, the increased reliance on communication infrastructure has also heightened the vulnerability of the power networks to cyber intrusions. Synchronized phasor data and GPS time-stamping used by Phasor Measurement Units (PMUs), make them prime targets for cyber intrusions. Among the different types of intrusions in smart grids, Time Synchronization Attacks (TSA), because of their impact and easier execution, are widely employed by intruders to disrupt grid operations. Such attacks aim at spoofing GPS signals, thereby altering voltage and current phasor information across the network. The same leads to malfunction of the operations executed at the control center. The present work aims to develop a secured and resilient mechanism against TSAs in smart grids. In this regard, a two-stage mechanism based on deep learning and spline interpolation is proposed. The first stage employs an LSTM-based classifier to detect TSAs in the cyber layer. Post-TSA detection, the second stage uses spline interpolation to filter out malicious data. The filtering allows for the restoration of the actual pre-TSA data acquired from PMUs. The proposed TSA detection and correction scheme has been validated extensively across various TSA scenarios on IEEE 9, 14, and 57 bus systems. Majority of the reported works of TSA detection have been validated using offline numerical simulations, which have limitations in replicating practical TSA dynamics. To address the same, the proposed scheme has been validated using a real-time testbed comprising of a digital simulator, real PMU, GPS receiver, and a data acquisition module with a communication interface.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115647"},"PeriodicalIF":5.3,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.chaos.2024.115632
Donghua Jiang , Zeric Tabekoueng Njitacke , Guoqiang Long , Jan Awrejcewicz , Mingwen Zheng , Lei Cai
Currently, the latest advances in artificial neural networks have deeply affected various aspects of the general public. To this end, a new Tabu Learning Neuron (TLN) model with variable activation gradients is proposed in this paper. Specifically, its kinetic behaviors and intrinsic properties are investigated by means of a two-parameter Lyapunov exponential spectrum, a bifurcation and an equilibrium point analysis. Moreover, its electronic circuit built in the PSpice environment agrees with the numerical results. Besides, in respect of its engineering applications, a novel data compression-encryption scheme based on the new TLN model, matrix factorization theory and compressive sensing technology is introduced for providing a secure data exchange environment in the healthcare community. Finally, performance evaluation indicates that the proposed cryptography scheme has remarkable advantages in terms of reconstruction quality and security.
{"title":"Novel Tabu learning neuron model with variable activation gradient and its application to secure healthcare","authors":"Donghua Jiang , Zeric Tabekoueng Njitacke , Guoqiang Long , Jan Awrejcewicz , Mingwen Zheng , Lei Cai","doi":"10.1016/j.chaos.2024.115632","DOIUrl":"10.1016/j.chaos.2024.115632","url":null,"abstract":"<div><div>Currently, the latest advances in artificial neural networks have deeply affected various aspects of the general public. To this end, a new Tabu Learning Neuron (TLN) model with variable activation gradients is proposed in this paper. Specifically, its kinetic behaviors and intrinsic properties are investigated by means of a two-parameter Lyapunov exponential spectrum, a bifurcation and an equilibrium point analysis. Moreover, its electronic circuit built in the PSpice environment agrees with the numerical results. Besides, in respect of its engineering applications, a novel data compression-encryption scheme based on the new TLN model, matrix factorization theory and compressive sensing technology is introduced for providing a secure data exchange environment in the healthcare community. Finally, performance evaluation indicates that the proposed cryptography scheme has remarkable advantages in terms of reconstruction quality and security.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115632"},"PeriodicalIF":5.3,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535219","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}
This work uses a reaction–diffusion system to explore self-organized pattern-forming phenomena through species distribution in a tri-trophic food web system. The interacting non-diffusive system involves a bottom prey, one specialist intermediate predator dependent on the bottom prey, and a generalist top predator, having its food preference regulation on both the bottom prey and intermediate predator. The system encounters temporal instability through Hopf-bifurcation and chaotic oscillations about the coexistence equilibrium with over-dependency on a particular food source. We provide analytical conditions for diffusion-driven Turing and wave instabilities. A weakly nonlinear analysis (WNA) is performed to examine the patterns of Turing instability close to the critical threshold. Numerical simulations show spatiotemporal patterns like spots, stripes, a mixture of spots & stripes and spatiotemporal chaos. The numerical investigations highlight the non-Turing instabilities consisting of Hopf, wave, Hopf-Turing, Hopf-wave. The diffusion of species suppresses regular and irregular spatiotemporal oscillations, giving stability to the system. Using a heat map of the Lyapunov exponents of the time series for different pairs of parameter values in a bi-parametric plane, it is demonstrated that the Turing pattern dominates the oscillatory Hopf pattern if the critical parameter value is from the Hopf-Turing region and is close to the Hopf bifurcation threshold, but the Hopf pattern dominates if the parameter pair is significantly away from it. The qualitative comparison of the non-Turing instabilities is provided with the corresponding spatiotemporal distribution of the species. It is observed that the high-amplitude oscillations of Hopf and Hopf-dominated non-Turing oscillations are vicious for the spatially distributed population.
{"title":"Diffusion-driven instabilities in a tri-trophic food web model: From Turing to non-Turing patterns and waves","authors":"Bhaskar Chakraborty , Sounov Marick , Nandadulal Bairagi","doi":"10.1016/j.chaos.2024.115634","DOIUrl":"10.1016/j.chaos.2024.115634","url":null,"abstract":"<div><div>This work uses a reaction–diffusion system to explore self-organized pattern-forming phenomena through species distribution in a tri-trophic food web system. The interacting non-diffusive system involves a bottom prey, one specialist intermediate predator dependent on the bottom prey, and a generalist top predator, having its food preference regulation on both the bottom prey and intermediate predator. The system encounters temporal instability through Hopf-bifurcation and chaotic oscillations about the coexistence equilibrium with over-dependency on a particular food source. We provide analytical conditions for diffusion-driven Turing and wave instabilities. A weakly nonlinear analysis (WNA) is performed to examine the patterns of Turing instability close to the critical threshold. Numerical simulations show spatiotemporal patterns like spots, stripes, a mixture of spots & stripes and spatiotemporal chaos. The numerical investigations highlight the non-Turing instabilities consisting of Hopf, wave, Hopf-Turing, Hopf-wave. The diffusion of species suppresses regular and irregular spatiotemporal oscillations, giving stability to the system. Using a heat map of the Lyapunov exponents of the time series for different pairs of parameter values in a bi-parametric plane, it is demonstrated that the Turing pattern dominates the oscillatory Hopf pattern if the critical parameter value is from the Hopf-Turing region and is close to the Hopf bifurcation threshold, but the Hopf pattern dominates if the parameter pair is significantly away from it. The qualitative comparison of the non-Turing instabilities is provided with the corresponding spatiotemporal distribution of the species. It is observed that the high-amplitude oscillations of Hopf and Hopf-dominated non-Turing oscillations are vicious for the spatially distributed population.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115634"},"PeriodicalIF":5.3,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.chaos.2024.115655
Qianxue Wang, Dongsheng Kuang, Simin Yu
This paper designs the simplest -dimensional () digital chaotic system using a strongly connected graph inverse approach. Compared to previous systems, this approach significantly simplifies the system structure while enhancing statistical performance. First, in the -dimensional digital iterative system, we construct -state transition graph with bidirectional direct paths between any two states. Under the condition that the bitwise XOR result between any two states equals the combination of the current unilateral infinite sequence outputs, we derive the corresponding simplest uncoupled -dimensional iterative functions based on the inverse approach. Second, based on the simplest uncoupled -dimensional iterative functions, we develop a cascaded closed-loop coupling approach to obtain the corresponding simplest fully coupled -dimensional iterative functions, theoretically proving that they satisfy Devaney’s chaos definition. Compared to previous systems, this closed-loop coupling method not only simplifies the system structure, making it the simplest form among all fully coupled -dimensional iterative functions, but also significantly improves statistical performance, as evidenced by passing both NIST and TestU01 tests. Finally, we validate the effectiveness and superiority of the simplest -dimensional digital chaotic system through circuit design and FPGA simulation experiments.
本文利用强连接图逆方法设计了最简单的 m 维（m=2,3,4,...）数字混沌系统。与以往的系统相比，这种方法大大简化了系统结构，同时提高了统计性能。首先，在 m 维数字迭代系统中，我们构建了 2m 状态转换图，任意两个状态之间都有双向直接路径。在任意两个状态之间的比特XOR结果等于当前m个单边无穷序列输出组合的条件下，我们基于逆方法推导出相应的最简单的非耦合m维迭代函数。其次，在最简单的非耦合 m 维迭代函数的基础上，我们开发了一种级联闭环耦合方法，得到了相应的最简单的完全耦合 m 维迭代函数，并从理论上证明了它们满足 Devaney 的混沌定义。与以前的系统相比，这种闭环耦合方法不仅简化了系统结构，使其成为所有全耦合 m 维迭代函数中最简单的形式，而且显著提高了统计性能，通过 NIST 和 TestU01 测试就是证明。最后，我们通过电路设计和 FPGA 仿真实验验证了最简单 m 维数字混沌系统的有效性和优越性。
{"title":"Generating digital chaotic systems of the simplest structure via a strongly connected graph inverse approach","authors":"Qianxue Wang, Dongsheng Kuang, Simin Yu","doi":"10.1016/j.chaos.2024.115655","DOIUrl":"10.1016/j.chaos.2024.115655","url":null,"abstract":"<div><div>This paper designs the simplest <span><math><mi>m</mi></math></span>-dimensional (<span><math><mrow><mi>m</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>…</mo></mrow></math></span>) digital chaotic system using a strongly connected graph inverse approach. Compared to previous systems, this approach significantly simplifies the system structure while enhancing statistical performance. First, in the <span><math><mi>m</mi></math></span>-dimensional digital iterative system, we construct <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup></math></span>-state transition graph with bidirectional direct paths between any two states. Under the condition that the bitwise XOR result between any two states equals the combination of the current <span><math><mi>m</mi></math></span> unilateral infinite sequence outputs, we derive the corresponding simplest uncoupled <span><math><mi>m</mi></math></span>-dimensional iterative functions based on the inverse approach. Second, based on the simplest uncoupled <span><math><mi>m</mi></math></span>-dimensional iterative functions, we develop a cascaded closed-loop coupling approach to obtain the corresponding simplest fully coupled <span><math><mi>m</mi></math></span>-dimensional iterative functions, theoretically proving that they satisfy Devaney’s chaos definition. Compared to previous systems, this closed-loop coupling method not only simplifies the system structure, making it the simplest form among all fully coupled <span><math><mi>m</mi></math></span>-dimensional iterative functions, but also significantly improves statistical performance, as evidenced by passing both NIST and TestU01 tests. Finally, we validate the effectiveness and superiority of the simplest <span><math><mi>m</mi></math></span>-dimensional digital chaotic system through circuit design and FPGA simulation experiments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115655"},"PeriodicalIF":5.3,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.chaos.2024.115631
Yinuo Wang , Chuandong Li , Hongjuan Wu , Hao Deng
In this paper, considering that the limited speed of information transfer may generate time delay, which can sometimes influence the stability of the system, but in reality time delay is pervasive, and sometimes can have a positive impact on system’s stability, so it is essential to think about its existence. The nonlinear systems under delayed impulsive control (IC) are investigated here, and we mainly utilize the multiple-spans step-function method to analyse the stability conditions of the considered systems, which can be counted as a generalization of the Lyapunov-like stability method and is less conservative compared with the existing traditional Lyapunov-like function method. Moreover, it is the first time that this method employed for the stability of systems with IC and time delay. Two examples of equidistant impulses of nonlinear autonomous system and non-equidistant impulses of linear time-varying system by using two-spans step-function method are presented to validate the utility of the presented approach, respectively. Besides, the Zeno behavior of autonomous system without time delay is provided and treated by the presented method, which can better manifest the extensive viability of the method compared with the Lyapunov-like function method.
本文考虑到信息传递速度有限可能会产生时延，时延有时会影响系统的稳定性，但实际上时延无处不在，有时会对系统的稳定性产生积极影响，因此有必要思考时延的存在。本文研究了延迟脉冲控制（IC）下的非线性系统，主要利用多跨阶跃函数法分析了所考虑系统的稳定性条件，该方法可以算作是类李雅普诺夫稳定性方法的广义化，与现有的传统类李雅普诺夫函数法相比，其保守性较低。此外，该方法还首次用于具有 IC 和时延的系统的稳定性。本文以非线性自主系统的等距脉冲和线性时变系统的非等距脉冲为例，分别验证了所提出方法的实用性。此外，提出的方法还提供并处理了无时延自主系统的 Zeno 行为，与 Lyapunov 类函数方法相比，更能体现该方法的广泛可行性。
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Pub Date : 2024-10-21DOI: 10.1016/j.chaos.2024.115648
Chen Chen , Lijie Wang
This article investigates the optimal output tracking problem for linear switched systems under DoS attacks. In contrast to early results which only consider the stability of switched systems under DoS attacks, the proposed control scheme can ensure the stability of the system while optimizing the system performance. Firstly, an augmented system is constructed based on the physical objects and command generator. Then, a Riccati equation of such an augmented system with DoS attacks is provided, and the optimal control scheme is obtained by iterative algorithm. Furthermore, to better align with practical scenarios, in this article, some restrictions on the instants of DoS attacks and switchings are removed, that is, multiple switchings are allowed during both active and inactive intervals of DoS attacks. In addition, the quantitative relationship regarding the duration and frequency of DoS attacks and the switching law is provided, which plays a key role in ensuring the stability of switching system under attacks. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.
本文研究了 DoS 攻击下线性开关系统的最优输出跟踪问题。与早期仅考虑 DoS 攻击下开关系统稳定性的研究成果相比，本文提出的控制方案既能保证系统的稳定性，又能优化系统性能。首先，根据物理对象和指令发生器构建一个增强系统。然后，提供了这种具有 DoS 攻击的增强系统的 Riccati 方程，并通过迭代算法得到了最优控制方案。此外，为了更好地贴近实际应用场景，本文取消了对 DoS 攻击和切换时刻的一些限制，即在 DoS 攻击的活跃期和非活跃期都允许多次切换。此外，本文还提供了 DoS 攻击持续时间和频率与切换规律的定量关系，这对确保攻击下切换系统的稳定性起到了关键作用。最后，还提供了数值示例来证明所提方法的有效性。
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