Environmental effects on the dynamics of coupled nonlinear systems

Abstract

Most of the real world systems are complex and their dynamics is studied by modeling them by many subunits interacting with one another Such systems with interactions are well studied in the last few decades and are found to exhibit many emergent phenomena In real world situations the systems are not isolated but are in contact with some environment Studies of nonlinear systems in interaction with the environment are very rare There are many cases where the different dynamical activities are regulated monitored or triggered by a common medium or environment The actual mechanism in such cases are not fully understood and hence this forms a topic of great relevance for a detailed study In this thesis we report the study of emergent phenomena such as synchronization and amplitude death in nonlinear dynamical systems caused by coupling via a common shared environment We first consider a simple case where an environment interacts with two uncoupled chaotic systems The environment has an intrinsic damped dynamics of its own which is modulated via feedback from the systems The environment in turn gives feedback to both the systems Taking standard chaotic systems such as R quotossler and Lorenz systems as examples we show that such an interaction can be tuned to induce a variety of synchronization phenomena such as in phase anti phase complete and antisynchronization We then consider a case where two systems are coupled directly such that with sufficient strength of coupling they can exhibit synchronous behaviour The indirect feedback coupling through the environment is introduced in them in such a way as to induce a tendency for anti synchronization We show that for sufficient strengths these two competing effects can lead to amplitude death By choosing a variety of dynamics such as periodic chaotic hyperchaotic and time delay systems we illustrate that this mechanism is quite general and works for different types of direct coupling such as diffusive replacement and synaptic and different da newline newline