Feedback Control of Chaos and Hyper chaos

Abstract

Most of the natural systems are non-linear in nature and can exhibit irregular and complex behavior. Such complex dynamics, in general are termed as chaotic or hyper chaotic behavior, leading to irregular fluctuations and hence are not desirable inmost of the situations or applications. Hence there is an increasing interest in methods to control such complex behavior. In my project work, we have introduced a new control technique to quench such complex dynamical systems to steady state behavior. We numerically and analytically study the resultant properties of the system when coupled with an external damped system. We observe that for critical coupling coefficient, the complex behavior can be controlled to periodic or steady state dynamics. We find the value of the output result depends on the coupling coefficient values and by adjusting the damping coefficient, any desirable behavior can be obtained. We also study the nature of transition of different systems from a complex behavior to the steady state behavior. So also by adding a periodic dynamics in the control system, we can produce periodic behavior of a desired frequency in such complex systems.