2,312 publications from this institution
For the generalized Serre–Green–Naghdi system with weak Coriolis effect and surface tension, by using the dynamical system methods and singular traveling wave theory developed by Li and Chen [2007] to its associate traveling wave system, under different parameter conditions, all possible bounded solutions (solitary wave solutions, periodic wave solutions, peakons, periodic peakons as well as compacton solution families) are obtained. Exact explicit parametric representations are given.
No abstract is provided for this article.
Over the last two decades, multiwing chaos generation has seen promising advances and becomes an active research field today. It is well known that there is a gap between theoretical design and engineering applications in multiwing chaos generation. That is, most theoretical designs of multiwing chaotic attractors with mathematical proofs or numerical verification have rather complex expressions; however, most engineering applications of multiwing chaotic attractors without theoretical supports have simple expressions. To bridge the gap between theoretical design and engineering applications in multiwing chaos generation, this paper introduces a novel practical approach for generating grid multiwing butterfly chaotic attractors from the multipiecewise Lü system by constructing heteroclinic loops. It should be particularly pointed out that the designed multiwing chaotic attractors exhibit typical heteroclinic chaos from the heteroclinic Shil'nikov theorem and also have clear potential engineering applications. The proposed method can be easily extended to the generalized Lorenz system family.
This chapter focuses on leader-follower consensus of nonlinear multi-agent systems in homogenous networks and heterogenous networks via distributed impulsive control, respectively. Leader-follower consensus problem in homogenous networks is studied in Sect. 2. Then in Sect. 3, a network-based leader-following consensus problem is considered, and distributed delayed impulsive protocols are designed for nonlinear multi-agent systems. Finally, bounded leader-follower consensus problem is well investigated in heterogenous networks in Sect. 4. How to obtain a tight error bound, to optimize the error bound, and to design the impulse intervals and coupling strength within a prescribed error bound are addressed.
No abstract is provided for this article.
For three cubic–quartic optical soliton models of nonlinear refractive index together with nonlinear chromatic dispersion, the corresponding differential systems of the amplitude component are planar dynamical systems with a singular straight line. In this paper, by using the techniques from dynamical systems developed by Li & Chen, 2007 to analyze the parameter conditions of systems and construct the corresponding phase portraits, the dynamical behavior of the amplitude component can be analyzed. Under different parameter conditions, exact explicit envelope solitary wave solutions, periodic wave solutions, periodic peakons as well as the peakon solution, can all be found.
In this paper, a simple fuzzy logic based intelligent mechanism is developed for predicting and controlling a chaotic system to a desired target, using only input–output data obtained from the unknown (or uncertain) underlying chaotic system. In the chaos prediction phase, a fuzzy system approach incorporating with Gaussian type of fuzzy membership functions is used. Only system input–output data are needed for prediction, and a recursive least-squares computational algorithm is employed for the calculation. In the controller design phase, the Lyapunov stability criterion is used, which forms the basis of the main design principle. Some simulation results on the chaotic Sin map and Hénon map are given, for both prediction and control, to illustrate the effectiveness and control performance of the proposed method.
This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.
Experimental studies have shown that neuron population located in the basal ganglia of parkinsonian primates can exhibit characteristic firings with certain firing rates differing from normal brain activities. Motivated by recent experimental findings, we investigate the effects of various stimulation paradigms on the firing rates of parkinsonism based on the proposed dynamical models. Our results show that the closed-loop deep brain stimulation is superior in ameliorating the firing behaviors of the parkinsonism, and other control strategies have similar effects according to the observation of electrophysiological experiments. In addition, in conformity to physiological experiments, we found that there exists optimal delay of input in the closed-loop GPtrain|M1 paradigm, where more normal behaviors can be obtained. More interestingly, we observed that W-shaped curves of the firing rates always appear as stimulus delay varies. We furthermore verify the robustness of the obtained results by studying three pallidal discharge rates of the parkinsonism based on the conductance-based model, as well as the integrate-and-fire-or-burst model. Finally, we show that short-term plasticity can improve the firing rates and optimize the control effects on parkinsonism. Our conclusions may give more theoretical insight into Parkinson's disease studies.
A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.
In this paper, a new structure of predictive fuzzy PID controller is proposed. The new controller is robust and effective in controlling higher order and time-delayed complex processes. The proposed predictive fuzzy PID controller combines the fuzzy PID and generalized predictive control (GPC) ideas together, and is equipped with optimization capability that minimizes a cost function. These features make the new controller more effective than individual fuzzy PID and GPC controllers in handling nonlinear systems. Computer simulations are shown for various types of process stabilization and set point tracking problems.
No abstract is provided for this article.
−− The output behavior of a nonlinear control system depends not only on its input but also on its initial conditions. These two factors have to be considered simultaneously in nonlinear systems design. This paper presents a new definition, called dynamic right factorization, for nonlinear dynamic control systems. This factorization takes the initial conditions as well as the system input into account. Coprimeness and fundamental properties of dynamic right coprime factorization are investigated. Its relations to the system observability and the observer design problem are discussed. An example is given to illustrate the procedure of obtaining the dynamic right factorization and designing an observer for a given nonlinear dynamic system.
This paper addresses the distributed H ∞ consensus problem of linear or linearized multi-agent systems subject to external disturbances. A distributed consensus protocol is proposed, based on the relative states of neighboring agents. The distributed H ∞ consensus problem of such a multi-agent network is cast into the H ∞ control problem of a set of independent systems having the same dimension as that of a single agent. The notion of H ∞ consensus region is then introduced and analyzed. A necessary and sufficient condition for the existence of a protocol having an unbounded H ∞ consensus region is derived. A multi-step procedure is further presented for constructing such a protocol. It is shown that the H ∞ performance limit of the consensus of the multi-agent network is equal to the minimal H ∞ norm of a single agent achieved by using a state feedback controller.
In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, “period three implies chaos” for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li–Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived.
No abstract is provided for this article.
No abstract is provided for this article.
This paper describes two basic structures for identifying chaotic systems based on the Wiener and Hammerstein cascade models, in which three-layer feedforward artificial neural network is employed as the nonlinear static subsystem and a simple linear plant is used as the dynamic subsystem. Through training of the neural network and choosing an appropriate linear subsystem, various chaotic systems can be well identified by these two basic structures. Computer simulation results on Henon and Lozi systems are presented to demonstrate the effectiveness of these proposed structures. It is also shown that two chaotic systems whose outputs are different can actually exhibit similar chaotic attractors.
