Publications

Security Analysis of a Distributed Networked System Under Eavesdropping Attacks

In this brief, we consider the security problem for a network of linear time-invariant dynamical systems under eavesdropping attacks, where an eavesdropper can measure the states of some nodes in the network. We provide a necessary and sufficient condition for the eavesdropper to reveal the states of the networked system. We also present some necessary conditions for the case when the network has tail nodes or at least one node not monitored by the eavesdropper. In addition, we investigate several typical network structures and show that the networked system can be completely observed provided that the eavesdropper can monitor one node in each cycle. Further, we characterize the minimal set of necessarily monitored nodes with the upper bound set of such nodes. Finally, we verify the theoretical results by numerical simulations.

A bistable nonvolatile locally-active memristor and its complex dynamics

This paper introduces a novel bistable nonvolatile locally-active memristor model based on Chua's unfolding theorem to explore the influence of the local activity on the complexity of nonlinear systems. It is shown that the memristor has two asymptotically stable equilibrium points in its power-off plot with a negative memductance and a positive memductance, namely, it is nonvolatile. It is then shown that the fast switching between the two stable equilibrium points can be implemented by applying an appropriate voltage pulse. It is found that the memristor possesses four locally-active regions in its DC V-I plot, and a small signal equivalent circuit associated with a locally-active operating point of the memristor is designed using the small-signal analysis method, to explore its locally-active characteristics. Based on the small signal equivalent circuit, it is furthermore demonstrated that the nonvolatile locally-active memristor, when connected in parallel with a linear capacitor, oscillates periodically around a locally-active operating point via Hopf bifurcation. The dynamics of the memristor and its periodic oscillation are analyzed using the theory of local activity, pole-zero analysis of admittance functions, Hopf bifurcation and the edge of chaos. Finally, it is found that a chaotic oscillation evolved from the periodic oscillation appears by adding an energy-storage element (inductor) on the periodic oscillating circuit, which leads to the chaotic oscillation, coexisting attractors and various complex dynamical phenomena.

Observer-type Kalman innovation filter for uncertain linear systems

An observer-type of Kalman innovation filtering algorithm to find a practically implementable "best" Kalman filter, and such an algorithm based on the evolutionary programming (EP) optima-search technique, are proposed, for linear discrete-time systems with time-invariant unknown-but-hounded plant and noise uncertainties. The worst-case parameter set from the stochastic uncertain system represented by the interval form with respect to the implemented "best" filter is also found in this work for demonstrating the effectiveness of the proposed filtering scheme. The new EP-based algorithm utilizes the global optima-searching capability of EP to find the optimal Kalman filter and state estimates at every iteration, which include both the best possible worst case Interval and the optimal nominal trajectory of the Kalman filtering estimates of the system state vectors. Simulation results are included to show that the new algorithm yields more accurate estimates and is less conservative as compared with other related robust filtering schemes.

BIFURCATION DYNAMICS IN CONTROL SYSTEMS

This paper is to report the observation that when the popular time-delayed feedback strategy is used for control purpose, it may actually create unwanted bifurcations. Hopf bifurcation created by delayed feedback control is the main concern of this article, but some other types of bifurcations are also observed to exist in such delayed-feedback control systems. The observations are illustrated by computer simulations.

Scrambled sets of shift operators

In this paper, some characterizations about orbit invariants, p-scrambled points and scrambled sets are obtained.Applying these results solves a conjecture and two problems given in [X.Fu, Y. You,

An overview of bifurcation, chaos and nonlinear dynamics in control systems

This article offers a brief review of the fundamental concepts of bifurcation and chaos in nonlinear dynamical and control systems. Both the time-domain and frequency-domain versions of the classical Hopf bifurcation theory are studied in detail. Generalized (or degenerate) Hopf bifurcation is also discussed. Theoretical analysis and potential applications of the bifurcation theory in power systems are introduced. Meanwhile, chaos and the route to chaos from period-doubling bifurcations are described. In particular, chaos and bifurcations in feedback control systems and adaptive control systems are addressed. Because a nonlinear control system is by nature a very complex nonautonomous dynamical system due essentially to the involving of the control input, understanding and utilizing the rich dynamics of nonlinear control systems have an important impact in the modern technology. It calls for new effort and endeavor devoted to this scientific and engineering challenge.

Swarming behaviors in multi-agent systems with nonlinear dynamics

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.

Bifurcation and chaos of Chen's equation

Anti-control of chaos, making a non-chaotic system chaotic, has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen's equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen's equation, thereby revealing its different features from some other chaotic models such as the Lorenz system.

Indirect effects among biodiversity loss of mutualistic ecosystems

No abstract is provided for this article.

Design and implementation of fuzzy P 2 ID controller for handlebar control of a bicycle robot

This paper presents the design and implementation of a new fuzzy proportional-integration plus fuzzy proportional-derivative control scheme, named the fuzzy P 2 ID controller hereafter, for controlling the handlebar of a bicycle robot with time-varyi

Breaking a chaos-based secure communication scheme designed by an improved modulation method

Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919–24] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129–34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367–73], and Álvarez et al. [Álvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/0406065] via different attacks. As an enhancement to the Bu–Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu–Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

Coupled Discrete Fractional-Order Logistic Maps

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

Vehicle Miles Traveled Estimation Based on Taxi GPS Data: A Case Study in Nanjing, China

No abstract is provided for this article.

Degree-Distribution Stability of Growing Networks

In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the corresponding problems of growing network Markov chains. First we investigate the growing network Markov chains, and obtain the condition in which the steady degree distribution exists and get its exact formulas. Then we apply it to various growing networks. With this method, we get a rigorous, exact and unified solution of the steady degree distribution for growing networks.

Erratum to “An improved version of the Marotto theorem” [Chaos, Solitons and Fractals 18 (2003) 69–77]

A High Efficiency Multi-Stage Hierarchical Memory System with Realistic Behavior by Integrating DDR SDRAM Simulation Model

This study proposes a Verilog HDL based design for a high efficiency multi-stage hierarchical memory system with a double data rate synchronous dynamic random access memory (DDR SDRAM) simulation model as the main memory. In many mainstream modern computing systems, memory access speed and latency are major bottlenecks that limit master input of processor performance. These problems have become more pronounced as processor computing power increases while memory speeds fail to keep pace. At the same time, also hoping that the main memory can be a DDR that is close to reality. To address these challenges, the proposed design introduces several key innovations. The overall system adopts a multi-stage hierarchical structure, which significantly reduces delays caused by the speed gap between the input and main memory to the greatest extent. Additionally, optimized memory control and scheduling strategies are employed through advanced timing control and command scheduling. Also, a DDR simulation model is integrated as the main memory, offering a realistic representation of data flow and access patterns. This model helps to accurately predict and validate memory control strategies under various real-world conditions. Through complete design and integration of these blocks, the system's performance is significantly enhanced, demonstrating improved efficiency in memory management and data transmission. This design lays the foundation for the future development of memory systems and provides a promising solution for the next generation of high efficiency computing environments.

Complex Symbolic Dynamics of Chua's Period-2 Rule 37.

No abstract is provided for this article.