Oscillation Quenching In Coupled Nonlinear Oscillator Systems

Oscillation quenching constitutes a fundamental emergent phenomenon in systems of coupled nonlinear oscillators, which is widely applied in some biological, chemical and physical systems recently. At the same time, it plays a important role in our real life,therefore it is very meaningful for us to study the oscillation quenching phenomenon. In this thesis, we pay special attention to the study of two structurally distinct oscillation quenching types: oscillation death(OD) and amplitude death(AD) phenomena.In the first chapter, we introduce the research background and significance of coupled nonlinear oscillators. Then the basic concepts and research progresses of OD and AD are introduced in detail. In the second chapter, we systematically investigate bifurcation analysis for the homogeneous and inhomogeneous steady states of coupled StuartLandau oscillators with the diffusive coupling scenarios. In the third chapter, we study bifurcation analysis for the inhomogeneous steady states of coupled Brusselators with the diffusive coupling scenarios. In the fourth chapter, we aim to set clear boundaries between these two very different oscillation quenching manifestations and demonstrate the importance for their correct identification from the aspect of theory as well as of application. we also discuss the transition from amplitude to oscillation death in coupled oscillators and the dynamical mechanisms of AD and OD in identical coupled oscillators.The paper uses linear analysis and numerical calculation of the steady states. If real part of the whole eigenvalues are negative, the steady states will be stable.The end of this article is a summary about the phenomena of amplitude death and oscillation death in coupled nonlinear systems.