{"title":"A resilient event-triggered control strategy for truck platooning cyber–physical systems against denial-of-service attacks","authors":"","doi":"10.1016/j.chaos.2024.115424","DOIUrl":"10.1016/j.chaos.2024.115424","url":null,"abstract":"<div><p>With the deployment of vehicle-to-everything(V2X) communication technology, Denial-of-Service(DoS) attacks gradually pose potential threats for the truck platooning cyber–physical systems(TPCPS) due to disruption of information exchange in vehicular networks, resulting in instability of truck platooning and even traffic accidents. Motivated by this, the study proposes a resilient event-triggered control strategy to maintain the performance or stability of the TPCPS when DoS attacks happen. First, a resilient event-triggered mechanism is proposed to ensure that the onboard controller can receive and update status information in time after attack intervals, mitigating effect of the vehicle-to-vehicle(V2V) communication disruptions. Subsequently, the sufficient condition is derived which is to confine DoS attacks and makes a key role in maintaining the platoon’s internal stability. To guarantee the consensus control performance of the TPCPS, the switched event-triggered controller is designed by the Lyapunov approach. The controller is expected to output corresponding control based on the updated status information in communication interval. Ultimately, the proposed strategy’s effectiveness is validated through simulations. The proposed resilient event-triggered control strategy is shown to be able to effectively mitigate abnormalities in the TPCPS under DoS attacks, thus ensuring safe and comfortable driving. Compared with event-triggered sliding mode control, the proposed method achieves smaller inter-vehicle distances while ensuring stability, enhancing traffic efficiency.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076627","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}
{"title":"Matryoshka multistability: Coexistence of an infinite number of exactly self-similar nested attractors in a fractal phase space","authors":"","doi":"10.1016/j.chaos.2024.115412","DOIUrl":"10.1016/j.chaos.2024.115412","url":null,"abstract":"<div><p>Multistability, and its special types such as megastability and extreme multistability, is an important phenomenon in modern nonlinear science that provides several possible practical applications. In this paper, we propose a new special type of multistability when the infinite number of exactly self-similar attractors nested inside each other coexist in a system. We called it matryoshka multistability due to its resemblance to the famous Russian wooden doll. We theoretically explain and experimentally confirm the properties of a new type of multistable behavior using two representative examples based on the Chua and Sprott Case J chaotic systems. In addition, we construct an adaptive controller for synchronizing two Chua-type matryoshka multistable systems when the amplitude of the master system is of arbitrary scale. The proposed type of multistability can find several applications in chaotic communication, cryptography, and data compression.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076630","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}
{"title":"Deep Learning models for the analysis of time series: A practical introduction for the statistical physics practitioner","authors":"","doi":"10.1016/j.chaos.2024.115359","DOIUrl":"10.1016/j.chaos.2024.115359","url":null,"abstract":"<div><p>Following other fields of science, Deep Learning models are gaining attention within the statistical physics community as a powerful and efficient way for analysing experimental and synthetic time series, and for quantifying properties thereof. Applying such models is nevertheless a path full of pitfalls, not only due to their inherent complexity, but also to a lack of understanding of some of their idiosyncrasies. We here discuss some of these pitfalls in the context of time series classification, covering from the selection of the best model hyperparameters, how the models have to be trained, to the way data have to be pre-processed. While not providing one-fits-all answers, the statistical physics practitioner will here find what questions ought to be posed, and a first guide about how to tackle them.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0960077924009111/pdfft?md5=2d2c869e19b00890a513ae3af6205064&pid=1-s2.0-S0960077924009111-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076629","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}
{"title":"Semi-visual obfuscation image encryption algorithm based on π-type chaotic amplifier and self-hiding fuzzy","authors":"","doi":"10.1016/j.chaos.2024.115402","DOIUrl":"10.1016/j.chaos.2024.115402","url":null,"abstract":"<div><p>The level of privacy may vary across different parts of an image. This paper proposes a semi-visual obfuscation algorithm for images that takes into account the varying levels of privacy in different areas of the image. Firstly, we present a novel One-dimensional Uniform Chaotic Amplifier (1_DUCA) aimed at expanding the parameter range and enhancing the uniformity of the standard one-dimensional chaotic map. Next, we employ a detection algorithm or autonomous frame selection to identify the precise location of the area with strong privacy. Finally, we apply noise to blur the selected area and conceal vital bit information within the image. At this point, the image has certain visual effects, and only people with prior knowledge can recognize the image. Furthermore, in the last stage of image encryption, we employ a weight scrambling and high-low bit coupled diffusion technology to completely obscure the visual effects of the image. It is noteworthy that the experimental results and performance analysis have verified the practicality and security of the encryption algorithm. Moreover, they have also demonstrated the robust amplification effect of the employed amplifier.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076631","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}
{"title":"A conjugate method for simulating the dynamics of stochastic urban spatial network models","authors":"","doi":"10.1016/j.chaos.2024.115430","DOIUrl":"10.1016/j.chaos.2024.115430","url":null,"abstract":"<div><p>Urban networks are integral components of urban systems, contributing to their functioning and shaping the overall dynamics of urban areas. They are characterized by their complexity, interdependence, and dynamic nature. The construction, analysis and understanding of urban network models is therefore essential to address complex urban challenges, fostering sustainable development, and improving the overall quality of life in systems like cities and regions. In this work, we present and analyze the properties of a stochastic spatial-interaction model of urban structures. In addition, we devise a suitable time-stepping integrator that allows analyzing the evolution of this stochastic system at large times intervals, providing information of the dynamical behavior of the system in its equilibrium state. Numerical simulation studies are carried out to illustrate the practical effectiveness of the proposed approach.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049450","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}
{"title":"The impact of conditional coupling based on environment comparison between interdependent networks on the evolution of cooperation","authors":"","doi":"10.1016/j.chaos.2024.115427","DOIUrl":"10.1016/j.chaos.2024.115427","url":null,"abstract":"<div><p>The coupling between interdependent networks is a crucial factor affecting the evolution of cooperation. Actually, not all nodes in different sub-networks of the interdependent network can establish a one-to-one corresponding coupling relationship, and whether the connection between corresponding nodes can be built is often related to the local environment and global environment where the individual is located. Therefore, we explore how the conditional coupling between interdependent networks based on the comparisons of local and global environments affects the spread of cooperative behavior. We consider two types of conditional coupling modes: static coupling and dynamic coupling. The classic prisoner’s dilemma is chosen as the fundamental game model. The numerical simulation results on the interdependent network constructed by square lattices show that conditional coupling based on environmental comparison favors the propagation of cooperation, regardless of the type of conditional coupling. And the promotion level of cooperation is proportional to the coupling strength. Moreover, we further perform the simulation experiments on the interdependent networks composed of ER (Erdös–Rényi) random networks. Our explorations may be helpful for understanding the survival and maintenance of cooperation in the interconnected and interrelated systems.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049448","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}
{"title":"Optimal control problem governed by a kind of Kirchhoff-type equation","authors":"","doi":"10.1016/j.chaos.2024.115422","DOIUrl":"10.1016/j.chaos.2024.115422","url":null,"abstract":"<div><p>In this paper, we consider an optimal control problem governed by a kind of Kirchhoff-type equation, which plays an important role in the phenomenon of beam vibration. Firstly, the existence of solution to the state equation is proved by the variational method. Secondly, for the given cost functional, we get that there exists at least an optimal state-control pair via the Sobolev’s embedding theorem under the constraint of the state equation. Next, the necessary optimality condition for the optimal solution is derived by using the cone method. Finally, we give the pointwise variational inequality, minimum principles and an equivalent necessary condition for the optimal control problem according to the discussion of the variational inequality.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045821","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}
{"title":"Predefined time quasi-sliding mode control with fast convergence based on a switchable exponent for nonlinear systems","authors":"","doi":"10.1016/j.chaos.2024.115423","DOIUrl":"10.1016/j.chaos.2024.115423","url":null,"abstract":"<div><p>This paper proposed a new predefined time nonsingular sliding mode control (SMC) method for nonlinear systems. Firstly, based on the definition of predefined time stability (PTS), a new sufficient condition is designed to ensure that the system states converge to the origin within a predefined time. The design of a simple variable exponent not only guarantees PTS, but also enables adaptive adjustment when the system states are far away from and near the equilibrium point. And compared with traditional methods, the proposed <span><span>Lemma 2</span></span> enhances the control effect and achieves faster convergence whether the system states are far from or near to the equilibrium point. Secondly, based on the proposed stability condition, a new nonsingular SMC method is designed to ensure that the tracking error converges to an arbitrarily small region within a predefined time. Finally, the proposed method is verified to have good performance through simulation and physical experiments.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045822","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}
{"title":"Fractional-order heterogeneous neuron network based on coupled locally-active memristors and its application in image encryption and hiding","authors":"","doi":"10.1016/j.chaos.2024.115397","DOIUrl":"10.1016/j.chaos.2024.115397","url":null,"abstract":"<div><p>Synaptic crosstalk significantly influences neural firing in the brain. Locally-active memristors can effectively emulate neural network synapses and have a significant importance in neural network research. This paper designs a tristable locally-active memristive model and presents a novel fractional-order (FO) heterogeneous neuron network. This neural network consists of Hindmarsh-Rose (HR) neuron and FitzHugh-Nagumo (FHN) neuron, which are connected by coupling FO locally-active memristors. The research found that changes in the order of different dimensions have a significant effect on the neural network firing through the three-parameter bifurcation diagram. Moreover, it is found that the locally-active memristor as a synapse can affect the coexistence firing behavior of the network. The complex dynamics have been studied numerically by using phase diagrams, Lyapunov exponent spectrum, bifurcation diagram and extreme multistability can be found. In particular, the system can generate a complex bursting behavior in the presence of an external current. In order to verify the accuracy of the simulation, the phase diagram of FO heterogeneous neuron network is implemented by STM32 microcontroller, and results of the experiments are in great agreement with results of the numerical simulations. Finally, an image encryption and hiding method based on FO heterogeneous neuron network and discrete wavelet transform (DWT) is proposed. The experimental results demonstrate that the encryption and hiding scheme has excellent security and strong robustness.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045824","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}
{"title":"On the stability of a single-species model with a generic delay distribution kernel","authors":"","doi":"10.1016/j.chaos.2024.115425","DOIUrl":"10.1016/j.chaos.2024.115425","url":null,"abstract":"<div><p>The delayed logistic equation, also known as Hutchinson’s equation, is a simple and elegant model commonly used to capture critical features of complex phenomena in biology, medicine, and economics. This paper studies the stability of a single-species logistic model with a general delay distribution and a constant inflow of nutritional resources. We provide conditions for the linear stability of the positive equilibrium and the occurrence of Hopf bifurcation. The findings complement existing literature and are applied to specific delay distributions: Uniform, Dirac-delta, and gamma distributions. Without resource inflow, we find that the positive equilibrium is stable for short delays but loses stability through Hopf bifurcation as the mean delay increases. The model’s dynamics vary with resource inflow based on the delay distribution: in uniform and Dirac-delta distributions, the dynamics are similar to the no-inflow case, whereas for the gamma distribution, stability depends on the delay order <span><math><mrow><mi>p</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049449","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}