Amplitude Death In Coupled Nonlinear Oscillator Systems

Complex systems in reality are often nonlinear, and can be regarded as many coupled subsystems. Affected by the coupling structure, coupling ways and others,the whole system performs abundantly dynamical behaviors. Study these behaviors not only can help people understanding natural phenomenons, but also have actual application values. The amplitude which stay a suppressed state, is amplitude death. Induce the amplitude death is a way for system stabilization, and is a effective mechanism for dynamical control, so it has a very good application value.The present paper shows that dynamic coupling induces amplitude death in coupled identical nonlinear oscillators. First, we consider two coupled identical oscillators, then many. Using a linear analysis, the paper find a stability condition in theory for amplitude death in dynamical coupled systems. Afterwards, we separately applied our stability analysis results into coupled Stuart-Landau systems, Lorenz systems and R(?)ssler systems in detail. The numerical simulations on the basis of Routh stability criterion and Segment Lemma make us derive the parameter space in which amplitude death occurs and let us confirm the death island.At the end of the article, we made a summary and a outlook.