The Dynamics In The System Of Coupled Oscillators

The collective behavior in a system composed of a large number of elements has attracted the attention and research of scholars in many fields.In the past few decades,a large number of studies on nonlinear dynamic systems have emerged,especially the discovery of many interesting dynamic states in the system of coupled oscillators,which has led more and more scholars to pay attention to the subject of nonlinear dynamics.Among them,the chimera state is a fascinating symmetry-breaking spatiotemporal pattern in a coupled oscillators network.Most previous studies chimera states have assumed that the modes of interaction between the oscillators or the positions of the oscillators in the system stationary.However,the time-dependent interaction mode or the existence of moving oscillators in the system changes the previous static assumptions.The study of chimera states in such systems is very interesting.Especially when the network space where the oscillator is located rises from one-dimensional space to two-dimensional space,it can been observed that more interesting results produced by the collision of chimera states.In this paper,we focus on the chimera state in a system of nonlocally coupled phase oscillators on a ring,and a system of the FitzHugh-Nagumo neurons in two-dimensional lattice network.Firstly,we introduce the basic theoretical knowledge of nonlinear dynamics and coupled phase oscillators.Secondly,we introduce the chimera state in the system of nonlocally coupled phase oscillator.Furthermore,the chimera states in the neuron oscillators systems are introduced in one-dimensional,two-dimensional and three-dimensional spaces,respectively.In the second chapter,we consider the system of nonlocally coupled phase oscillators under in a ring network.We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependently on the distance between them.We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag a and the agent mobility D.At the same time,we study the statistical characteristics of transient time and the mean lifetimes under different dynamic mechanisms.In Chapter 3,we consider the drift of chimera states in a ring of nonlocally coupled bicomponent phase oscillators.One part of the oscillators are stationary,and the others are moving at the velocity v along the ring.We find that different moving velocity will change the dynamic state of the system,and the interaction between the chimera states in the two oscillator group causes the the drift of chimera states.In Chapter 4,we consider a system of nonlocally coupled FitzHugh-Nagumo neuron oscillators in a two-dimensional lattice network.We find that the average phase velocity of coherent oscillators and incoherent oscillators in this system inconsistently.In the parameter space of the coupling radius R and the coupling phase ?,we have conducted more research on this inconsistency and the transformation.At the same time,the transitions of the dynamic state of the system caused by the coupling phase ? have been studied.We summarize the main results and present the prospect for future works in Chapter 5.