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This paper surveys some recent results about chaos induced by coupled-expanding maps. First, three typical definitions of chaos given by Li-Yorke, Devaney, and Wiggins, respectively, are introduced and compared. Then, several criteria of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces and in noncompact sets of complete metric spaces, respectively, are presented. Finally, some examples are provided for illustration.
<p>Recently, a necessary and sufficient condition for multivaluedness to be implicitly exhibited by counter-cascaded systems was presented. Subsequently, several systems that exhibit multivaluedness were reported. This brief interprets a general information transmission system as a counter-cascaded system with Shannon’s noisy-channel coding theorem providing the necessary and sufficient conditions for multivaluedness and is therefore a particular instance of the counter-cascaded network framework.</p>
In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.
This paper reports a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz, Rössler, Chen, Lü systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagrams. Analysis results show that this system has complex dynamics with some interesting characteristics.
Yang Sun, Guanrong Chen, Hamid Alinejad-Rokny, Jianzhu Bao, Yuqi Huang, Bin Liang, Kam-Fai Wong, Min Yang, Ruifeng Xu. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.
This is an essay to present some personal views onsystemsandnetworkswith respect to their similarities and differences as well as their relationships.
This paper studies delay-induced quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in second-order dynamics is designed where both the current and delayed position information is utilized. The time delay, in a common perspective, can induce periodic oscillations or even chaos to dynamical systems. However, it is surprisingly found in this paper that quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while it can be achieved with a relatively small time delay by appropriately choosing the coupling strength. A necessary and sufficient condition for reaching quasi-consensus in multi-agent dynamical systems is then established. It is further shown that quasi-consensus can be achieved if and only if the time delay is less than a critical value which depends on the coupling strengths and the largest eigenvalue of the Laplacian matrix of the network. Finally, a simulation example is given to illustrate the theoretical analysis.
This paper characterizes the complex dynamics of the permanent-magnet synchronous motor (PMSM) model with a non-smooth-air-gap, extending the work on the smooth case studied elsewhere. The stability, the number of equilibrium points, and the pitchfork and Hopf bifurcations are analyzed by using bifurcation theory and the center manifold theorem. Numerical simulations not only confirm the theoretical analysis results but also show some more new results including the period-doubling bifurcation, cyclic fold bifurcation, single-scroll and double-scroll chaotic attractors, ribbon-chaotic attractor, as well as intermittent chaos that are different from those reported in the literature before. Moreover, analytical expressions of an approximate stability boundary are given, by computing the local quadratic approximation of the two-dimensional stable manifold at an order-2 saddle point. Combining the existing results with the new results reported in this paper, a fairly complete description of the complex dynamics of the PMSM model is now obtained.
This paper reports a study of random deflection routing protocol and its impact on delay-jitter over packet networks. In case of congestion, routers with a random deflection routing protocol can forward incoming packets to links laying off shortest paths; namely, packets can be “deflected” away from their original paths. However, random deflection routing may send packets to several different paths, thereby introducing packet re-ordering. This could affect the quality of receptions, it could also impair the overall performance in transporting data traffic. Nevertheless, the present study reveals that deflection routing could actually reduce delay-jitter when the traffic loading on the network is not heavy.
As a spread spectrum communication system, code-shifted differential chaos shift keying (CS-DCSK) is required to provide reasonable bit error performance in a coexisting scenario where the conventional communication system is an interferer. Meantime, the bit error performance of the conventional communication system should not deteriorate dramatically in the presence of a CS-DCSK signal, which is as an interferer. This paper studies the performances of the CS-DCSK/BPSK coexisting system. By comparisons on the bit error rate (BER) of two coexisting systems, i.e., CS-DCSK/BPSK and DCSK/BPSK systems, in different channel environments at the same interference signal ratio, it reveals that CS-DCSK/BPSK has better performances than DCSK/BPSK. The BER expression of the CS-DCSK sub-system is derived in the presence of BPSK interference signals when two sub-systems are synchronized. Also derived is the BER expression of the BPSK sub-system in the presence of CS-DCSK signals when two sub-systems are asynchronized and synchronized, respectively. For the synchronization case, the BER expression of the BPSK sub-system is independent of the strengths of CS-DCSK signals. As a new interferer, CS-DCSK has less effect on the conventional communication system. It is shown that numerical simulations are in good agreement with the analytic results.
A new approach is described for fuzzy modeling of control systems. It is shown that conventional concepts and criteria of stability and controllability of a control system can be extended to a fuzzy setting. More precisely, we establish a fuzzy dynamical model for nonlinear control system, that can be consistently applied to all linear multiinput/multioutput (MIMO) systems. This modeling is a fairly general representation of fuzzy control systems, and satisfies some natural extensions of the criteria such as stability and controllability, that conventional control experts use to evaluate a control system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
In this paper, we investigate the periodic orbits, spatial Lyapunov exponents, and stability of spatially periodic orbits of the general 2D Logistic system [Formula: see text] where a is a real constant and μ is a parameter. The existence of spatial chaos in the sense of Li and Yorke is proved using the Marotto theorem. These results extend the corresponding results in the 1D Logistic system [Formula: see text] where n 0 is a fixed integer. These results also improve some existing results of the 2D coupled map lattice (CML) model [Formula: see text] where ε > 0 is the coupling constant.
The information-based complexity of optimal reconstruction problems for general nonlinear systems is studied. Both lower and upper bounds for the worst-case reconstruction-error functional are given. The existence of an optimal reconstruction algorithm which achieves the infimum of the reconstruction-error is established.
In this paper, we aim to study the robust global exponential synchronization problem for a general class of Lur’e chaotic systems subject to time delays and impulsive disturbances. Furthermore, we also provide an estimation of the maximum Lyapunov exponent. By using the Lyapunov function method and linear matrix inequality (LMI) technique, sufficient conditions for the robust global exponential synchronization and estimation of its maximum Lyapunov exponent are obtained for the class of Lur’e chaotic systems with and without time delays, respectively. Furthermore, by applying the M-matrix theory, some of these sufficient conditions are shown to be expressible in forms of fairly simple algebraic conditions. For illustration, several examples are solved by using the sufficient conditions obtained.
