Amplitude Death In Conjugate Coupled Nonlinear Systems

Amplitude death is refers to oscillators stopping oscillating and stabilizing to the zero amplitude state through the interaction. AD is one of the collective behaviors in coupled nonlinear oscillators. And it is widely used in physical?biological and chemical. Therefore, analyzing amplitude death shows an important practical significance. In this paper, we focus on conditions of induction of amplitude death when dynamical oscillators are coupled by conjugate variable.The first chapter is the process of development of amplitude death and current situations home and abroad of this research subject. In the second chapter, we explore conditions of induction of amplitude death when two identical Landau-Stuart oscillators or Rossler oscillators are coupled via conjugate variable. In the third chapter, taking the Landau-Stuart system or Rossler system as the oscillator unit, respectively, we explore the conditions of induction of amplitude death when an infinite number oscillator is local conjugate coupled. In the fourth chapter, we study the conditions of induction of amplitude death when large number of oscillators, even if the oscillator number goes to infinity, is global conjugate coupled. I also get the transition relations between local and global coupling induced amplitude death. The end is a summary about the phenomena of amplitude death in coupled nonlinear oscillators by conjugate variable.