Study On The Kinetics Of Singularity And Synchronization In Coupled Discontinuous Systems

Recent years, the dynamics study of nonlocal coupled oscillators has been raised in the scientific community. It describes a system that each oscillator is interacted with the other oscillators, in addition, including the coupling strength decreases rapidly with increasing distance from them. it created a new dynamic phenomena "chimera state" in this new role, That is, the system is divided into two regions in a coupling effect, An area of the state is in Synchronization oscillator, another area in which oscillator is completely confused state, that is a Japanese physicist Kuramoto first discovered in study nonlocal coupling oscillator. It may explain some of the unique nature of animals behaviors, such as some birds、Lizards and dolphins, they sleep in the brain is "semi-sleep state". It was found that they awake part of the brain neurons in a chaotic state, and the other part of brain neurons asleep in a highly synchronized state, which sparked great interest of scientists.In this paper, we mainly discuss two important issues:A chimera states phenomenon with a discontinuous map in globally coupled oscillator model, The other one is to have a class to the small world network model in the two kinds of topology:three different image (i.e., simple topology kind tent map, logistic mapping and complex topology of discontinuous irreversible) shows rich dynamics behavior. In addition, the use of numerical simulation show that for simple topology mapping, dark lines is universal, but the method for complex topologies required further research, and the following conclusions can be given:(1) The third chapter of numerical simulation methods used to study the dynamic behaviors of a class of collective neither continuous nor reversible image composed of two mutually coupled subsystems:chimera state and cluster state, and calculate the change in the amplitude of space systems and the synchronization order parameter in respectively. Finally, the main parameters intervals of the chimera state or clusters states have been gotten. The results show that there are multiple chaotic attractors track in a chaotic state, State values of two subsystems evolve into chaotic orbit, whose value depends on not only a strict image discontinuity occurred after transition zone caused by iteration, and the most importantly, on the particular coupling strength between them, it is easy to track the states of the synchronization value in modulation under strong coupling. The strong coupling strength will help us determine the area of the system to achieve chaos synchronization control.(2) In a directed small-world networks, we calculated the value of the two topologies class research network (simple topology and complex topology), the choices of three images are more commonly studied:the tent map, logistic map and discontinuous mapping, and discussing the dependencies of their synchronization on coupling strength, connection probability, and fitting the correlation function of the critical coupling. Thus drawn:there is a critical function of a continuous map in universality class belongs to the sample topology, but it is not all belong to the complex topology, which is the presence of a great relationship with the intrinsic properties of an image, such as the zone area of discontinuous and irreversible combined effect oscillator network synchronization and lead to mutation.