2,312 publications from this institution
A new criterion is given for choosing the coupling constant in a system of coupled chaotic oscillators to guarantee their synchronization. The criterion is derived from a new observer design methodology based on Lyapunov stability theory. As an example and application, we prove the conjecture that synchronization of two chaotic Chua circuits can be achieved with the second state as the coupling variable provided that the coupling constant is suitably chosen according to the new criterion.
This paper further discusses the modified Marotto Theorem developed recently by Li and Chen (called “Marotto–Li–Chen Theorem” here for distinction). A simple yet rigorous chaotification (i.e., “anticontrol of chaos”) schemes is proposed for multi-dimensional dynamical systems based on the Marotto–Li–Chen Theorem. An illustrative example is included to show that the constructed chaotification algorithm is effective.
Abstract : This report presents a new digital redesign method for robust control of a sampled data uncertain system using an observer based digital controller. The multiple segment trapezoidal rule together with interval arithmetic is utilized to find a digital interval model of the original continuous time uncertain system. A dual concept of the digital interval modeling which captures the intersample states of the original continuous time uncertain system is used to discretize a predesigned continuous time state feedback robust controller so that the states of the digitally controlled continuous time uncertain system closely match those of the original analogously controlled continuous time uncertain system. A discrete time observer is constructed from the original continuous time observer such that the estimated states of the redesigned discrete time observer match those of the original continuous time observer at the sampling instants. Using the newly digitally redesigned observer based controllers, the resulting dynamic states of the digitally controlled sampled data uncertain systems are able to closely match those of the original analogously controlled continuous time uncertain systems.
The Hopf bifurcation theorem continuation of bifurcation curves on the parameter plane degenerate bifurcations in the space of system parameters high-order Hopf bifurcation formulas Hopf bifurcation in nonlinear systems with time delays birth of multiple limit cycles appendix.
For the optical soliton model in fifth-order weakly nonlocal nonlinear media, to find its exact explicit solutions, the corresponding traveling wave system is formulated as a planar dynamical system with a singular straight line. Then, by using techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze the planar system and find the corresponding phase portraits, the dynamical behavior of the amplitude component can be assessed. Under different parameter conditions, exact explicit solitary wave solutions, periodic wave solutions, kink, and anti-kink wave solutions, compacton solutions, as well as peakons and periodic peakons are found with precise formulations.
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological characteristics. Typical topological metrics are clustering coefficient, distance distribution, the largest eigenvalue of the adjacency matrix, and the gap between the first and the second largest eigenvalues, which are widely used to evaluate and compare different models of a network. In this paper, we show that evaluating complex network models based on the current topological metrics can be quite misleading. Taking several models of the AS-level Internet as examples, we show that although a model seems to be good to describe the Internet in terms of the aforementioned topological characteristics, it is far from being realistic to represent the real Internet in performances such as robustness in resisting intentional attacks and traffic load distributions. We further show that it is not useful to assess network models by examining some topological characteristics such as clustering coefficient and distance distribution, if robustness of the Internet against random node removals is the only concern. Our findings shed new lights on how to reasonably evaluate different models of a network, not only the Internet but also other types of complex networks.
This paper proposes a module-based and unified approach to chaotic circuit design, where the description is based on the state equations without physical dimensions for simplicity of a general discussion. The main design process consists of transformation of state variables, transformation from differential to integral operations, and transformation of the time-scale. The designed circuit consists of anti-adder module integrator module, and inverter module. A novel 3-scroll Chua's circuit and a generalized Lorenz-like circuit are designed and implemented for verifying the effectiveness of this systematic circuit design methodology. Experimental observations are provided for confirmation. Comparing with the traditional circuit design methods, this new design approach has the following typical characteristics: (i) module-based and unified design; (ii) independent adjustment of system parameters; (iii) adjustment of distribution regions for the frequency spectra of chaotic signals; (iv) prominent observability.
In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: 1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology, quite different from the familiar notion of consensus or formation controllability; 2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; 3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient. For a networked system with single-input/single-output (SISO) LTI nodes, we present precise necessary and sufficient conditions for the controllability of a general network topology.
No abstract is provided for this article.
This paper establishes some criteria of chaos in non-autonomous discrete systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover, several criteria of distributional chaos induced by coupled-expansion for an irreducible transition matrix are obtained. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts. One example is provided for illustration.
A new adaptive fuzzy control algorithm is developed in this paper, which has a regular fuzzy controller and a supervisory control term. This control algorithm does not require the system model, but has stability assurance for the closed-loop controlled system. The design is simple, in the sense that both the membership functions and the rule base are simple, yet generic. It can be applied to a large class of robotic and other mechanical systems.
Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a malicious attack. A framework of hierarchical attack is proposed, by means of edge- or node-removal attacks. Edges (or nodes) in a target network are classified hierarchically into categories, with different priorities to attack. The category of critical edges (or nodes) has the highest priority to be selected for attack. Extensive experiments on nine synthetic networks and nine real-world networks show the effectiveness of the proposed hierarchical attack strategies for destructing the network controllability. From the protection point of view, this study suggests that the critical edges and nodes should be hidden from the attackers. This finding helps better understand the network controllability and better design robust networks.
