Criteria Of Synchronization For Coupled Delay Partial Differential Systems

Synchronization phenomenon widely exists in complex systems. It is a kind ofcollective behavior of complex systems. The synchronization needs the final state ofeach node achieve consistence through the interaction between the systems. In recentyears, synchronization problem has become a research hotspot because of its importantpractical significance and broad application prospect. Due to the existence ofinformation communication, delay is always inevitable. Currently, few works werereported on the synchronization and robust H-infinity synchronization problem ofcoupled delay partial differential systems. The state of many motions in the real-worlddepends on not only time but also the space, such as nerve conduction, chemicalreactions, heat conduction and so on, these phenomena can be described as partialdifferential systems in mathematics. Motivate by the above statements, this article willstudy asymptotical synchronization problems and robust H-infinity synchronizationissues of coupled partial differential system.Firstly, the paper reviews the significance and research status of synchronizationissues. Then we studies asymptotical synchronization and robust H-infinitysynchronization issue of a class of quasi-linear second-order coupled delay partialdifferential systems. The cases of delay appearing in dynamic nodes and appearing indynamic nodes and coupling simultaneously are considered respectively. UsingLyapunov-Krasoviskii functional method and some techniques of the inequality, thesufficient conditions of coupled delay partial differential systems’ synchronization areprovided. When the external disturbance enters the coupled systems, the robustH-infinity synchronization is considered and sufficient conditions are provided.Then the paper discusses the synchronization problem of coupled delay partialdifferential systems with non-identical nodes. When the system has constant time delay,using Lyapunov-Krasoviskii functional method and some techniques of the inequality,the sufficient conditions for asymptotical synchronization and robust H-infinitysynchronization are put forwarded. When system has neutral delay, the sufficientconditions for asymptotical synchronization and robust H-infinity synchronization areprovided by similar method. In each part of the paper, numerical experiments are givento verify the correctness of the conclusions.