Controlling Dynamics of Nonlinear Oscillators through Linear Augmentation

Abstract

This thesis is consecrated to the study of controlling the dynamical newlinebehavior of the chaotic system through linear augmentation and aims to newlinecontribute a significant advancement by proposing a new control newlinescheme. The control scheme is exploited multifariously, such as for the newlinestabilization of the fixed point as well as to control the bistability 18 in a newlinebistable system. In addition, the ability of the control scheme is also newlinemanifested in logical computation and in the higher dimensional system. newlineRecently, the concept of indirect interaction between nonlinear newlineoscillators through the external environment was introduced. This type newlineof dynamical system model can explain several phenomena like quorum newlinesensing in bacteria or switching in genetic oscillators. In many biological newlineand chemical systems, coordinated. activity in a collection of systems newlinearises from interactions with molecules or chemicals distributed in a newlineshared environment or external medium. There have been. a few recent newlinestudies along this direction in which the occurrence of synchronized newlinestates, phenomena like phase flip, and amplitude death are shown as newlinecaused by an external system. A challenging question to answer is; Can newlinewe control the dynamical behavior of a single nonlinear dynamical newlinesystem when it is coupled to a linearly decaying system newline