For the case ofone-dimensional iterated mapswe present a new method for controlling deterministic chaos by the stabilization of one ofthe underlying unstable periodic orbits. The method works by applying a series of regular proportional feedbacks in the variable and does not require that the particular dynamical law is known. The method is illustrated with an application to the logistic and exp...

Following the development of the research on chaos and controlling chaos for ODEs, some methods and results of that for PDEs were developed in last decade. In this chapter, in addition to give a summary account in part, we present some results on controlling chaos for a class of parabolic type PDEs by applying the invariant manifold and structure stability theory. 1 Some Typical Models of PDEs ...

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube !TWT" amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction o...

Recent developments in engineering applications of stochastic resonance have expanded to various fields, especially biomedicine. Deterministic chaos generates a phenomenon known as chaotic resonance, which is similar resonance. However, are limited owing the problems controlling chaos, despite its uniquely high sensitivity weak signal responses. To tackle these problems, previous study proposed...

Since the beginning of the 90s a new direction appeared in the theory of dynamical systems, which was called “Controlling chaos”. The subject of this field is how to transform chaotic behavior to a regular one or to a more simple chaotic one by means of special small influence on the dynamical system. Pioneer works of this new direction were papers by Hubler and Lucher [1989], Jackson [1990] an...

In a recent paper [Phys. Rev. E 57 (1998) 1550] it was demonstrated that the symmetries of the evolution equation and the target state have a profound effect on controlling the chaotic behavior. In the present paper we extend these results to the cases of time-periodic target trajectories and inexact symmetries, and apply the developed formalism to the problem of controlling spatiotemporal chao...

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....