2,312 publications from this institution
The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási–Albert model and various star-shaped networks are performed for verification and illustration.
Controlling (or ordering) chaos is a new concept, which has recently drawn much attention from the communities of engineering, physics, chemistry, biomedical sciences and mathematics. This paper offers an overview of the different interpretations and approaches in the investigation of controlling chaos for various nonlinear dynamical systems. Relevant historical background is provided, several successful techniques are described and analyzed with necessary verifications, and some realistic yet instructive examples are included. The paper also aims at promoting more efforts to be devoted to this challenging and promising new direction of research, as well as its potential applications in nonlinear systems science and engineering.
In this paper, synchronization based parameter identification of dynamical systems from time series is carefully revisited. It is shown, based on rigorous theoretical analysis and concrete counterexamples, that some recent research reports on this issue are incomplete or even incorrect. A linear independence condition is pointed out, which is sufficient for such parameter identification of general dynamical systems.
In this paper, subgraphs and complementary graphs are used to analyze network synchronizability. Some sharp and attainable bounds are derived for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network’s corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.
No abstract is provided for this article.
Some new insights into the anti-phase synchronization of a network of inhibitorily coupled neurons are presented by means of qualitative analysis and numerical simulation. The network, which satisfies three significant conditions, gives rise to typical anti-phase synchronous solutions. By using the geometric method of dynamical systems, each corresponding reduced network model is analyzed, and a special and important parameter region, called P*-jumping up region, is identified. In terms of some basic properties of the P*-jumping up region, two conditions for the neuron states to enter this region are given. These conditions can be satisfied by adjusting a parameter K that controls the decay speed of the inhibitory coupling. Furthermore, it is concluded that if the parameter K is chosen so as to satisfy the two conditions, then two neurons will achieve anti-phase synchronous oscillation, independent of the initial conditions.
Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.
This paper reports the finding of the compound structure of a new chaotic attractor, which is obtained by merging together two simple attractors after performing a mirror operation. Furthermore, the forming mechanism of the new chaotic attractor is investigated.
In this paper, we present an approach for neural networks (NN) based identification of unknown nonlinear dynamical systems undergoing periodic or periodic-like (recurrent) motions. Among various types of NN architectures, we use a dynamical version of the localized RBF neural network, which is shown to be particularly suitable for identification in a dynamical framework. With the associated properties of localized RBF networks, especially the one concerning the persistent excitation (PE) condition for periodic trajectories, the proposed approach achieves sufficiently accurate identification of system dynamics in a local region along the experienced system trajectory. In particular, for neurons whose centers are close to the trajectories, the neural weights converge to a small neighborhood of a set of optimal values; while for other neurons with centers far away from the trajectories, the neural weights are not updated and are almost unchanged. The proposed approach implements a sort of "deterministic learning" in the sense that deterministic features of nonlinear dynamical systems are learned not by algorithms from statistical principles, but in a dynamical, deterministic manner, utilizing results from adaptive systems theory. The nature of this deterministic learning is closely related to the exponentially stability of a class of nonlinear adaptive systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.
No abstract is provided for this article.
Abstract : Most practical dynamical systems are formulated by hybrid uncertain delayed systems that consist of mixed continuous and discrete uncertain subsystems with state and/or input delays. For improving the performance of the delayed hybrid systems, well-established control theory and design methods are available in the continuous-time domain to find analog controllers. The resulting analog controller is required to be replaced by a digital controller for better reliability lower cost, smaller size, more flexibility and better performance. In this research, we have successfully accomplished the following research subjects: (1) Digital/analog model conversions of linear hybrid interval systems with unknown-but-bounded uncertain parameters; (2) Digital modeling and control of linear continuous-time systems with state, input and output delays; (3) Development of digital redesign techniques for digital control of cascaded linear hybrid interval systems; (4) Development of PAM (Pulse-Amplitude-Modulated) and PWM (Pulse-Width-Modulated) digital controllers for linear hybrid interval systems; (5) Design of digital PAM tracker for nominal chaotic orbits; (6) Interval Kalman filtering for linear stochastic uncertain systems; (7) Fuzzy-model-based self-tuning controller for nominal chaotic systems; (8) Model conversions and optimal control of 2D (2 Dimensional) nominal systems; (9) GA (Genetic Algorithm)-based optimal digital controllers for linear hybrid interval systems.
This paper presents some unusual dynamics of the Rabinovich-Fabrikant system, such as ``virtual'' saddles and ``tornado''-like stable cycles. Due to the strong nonlinearity and high complexity, the results are obtained numerically with some insightful descriptions and discussions.
