Controlling chaos is a topic in nonlinear dynamics which attracted a great deal of work in the last twenty years. Even though there are more definitions of the chaos [4], a distinctive characteristic of the chaotic behavior of a dynamical system is its sensitive dependence on the initial conditions. Generally, chaos is believed to be harmful because in many cases it can lead to disasters. Chaot...

This chapter presents an application of neural networks to chaos synchronization. The two main methodologies, on which the approach is based, are recurrent neural networks and inverse optimal control for nonlinear systems. On the basis of the last technique, chaos is first produced by a stable recurrent neural network; an adaptive recurrent neural controller is then developed for chaos synchron...

This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test called 0-1 test for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchron...

In this paper, the chaotic behavior of a set-valued mapping F : X → 2 , where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2 is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F , it is shown that the Bernoulli s...

In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of ch...

This paper deals with the control of chaos exhibited by an impacting mechanical oscillator of one-degree-of-freedom. Its mathematical model is represented by an impulsive hybrid non-autonomous linear dynamics. This dynamics can display attractive nonlinear phenomena such as bifurcations and chaos. In this paper, we propose an approach to control chaos. The proposed strategy is based primarily o...

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this techn...

– We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and...

This survey paper presents the state-of-the-art directional medium access control (MAC) protocols in wireless ad hoc and sensor networks (WAHSNs). The key benefits of directional antennas over omni-directional antennas are longer communication range, less multipath interference, more spatial reuse, more secure communications, higher throughput and reduced latency. However, directional antennas ...

Studies of nonlinear dynamical systems with many degrees of freedom show that the behavior of these systems is significantly different as compared with the behavior of systems with less than two degrees of freedom. These findings motivated us to carry out a survey of research focusing on the behavior of high-dimensional chaos, which include onset of chaos, routes to chaos, and the persistence o...