Multiple Synchronization Coexistence Phenomenon In Time-delay Systems

In this thesis, we explained systematically the controllable conditions, stability analysis and restrictions that involved in the control methods which can be divided into categories of feedback control and non-feedback control, according to its characteristics. Based on this, we studied the Open-plus-Close-Loop[1](OPCL)coupling in-depth and applied it into the time-delay systems.In the first place, we realized the CS, AS, AD and amplified(inverted) attractor in finite-dimensional systems with parameter mismatch or not. Typical numerical examples of a Hindamrsh-Rose model、Rossler system and Sprott system are given.In the second place, after analysis and discussion, we overcame the difficulties in extending the OPCL into systems of infinite-dimensional and advanced the form of OPCL. After that we used the extended synchronization method to realize multiple synchronization phenomenon in time-delay systems as below:1, we achieved CS,AS,AD and the attractor’s amplification, attenuation and inversion in optical bistable time-delay system with parameter mismatch or not.2, we,in particularly, realized arbitrary coexistence of the three coherent behaviors:stable complete synchronization, antisynchronization, amplitude death in Lorenz system with time-delay.3, By studying the process of transition to synchronization of mismatched time-delay systems, a scaling law is founded of independent of systems. At the same time, we also studied the phenomenon systematically.