Finite-Time Synchronization Of Coupled Reaction-Diffusion Systems

Complex networks exist in all aspects of life,such as the economic network,transport networks and power grids.Many reactions of physics and chemistry,such as nuclear reaction,groundwater seepage,heat conduction,whose state depends on not only time but also space,possess the diffusion phenomenon inevitably when the space of the system is uneven.Recently,it has been on the top of many scholars' research because of the important practical research significance.For the classification of synchronization,it can be divided into asymptotical synchronization and finite-time synchronization based on the time that system achieves synchronization.Compared to asymptotic synchronization,finite-time synchronization is highly valued in the engineering and other fields because of the finite and computable synchronization time.There exist large data which need to be transmitted,while the finite switching speed and the limited speed of the node itself make the time delay appear inevitably.In this paper,the full-domain control,boundary control and pinning control will respectively be used to enable the system to achieve finite-time synchronization status.In this paper,finite-time synchronization is considered for coupled reaction-diffusion systems with time-varying delays.By designing full-domain controller and using Lyapunov-Krasovskii functional and LMI inequality,adequacy criteria of finite-time synchronization are obtained.And we give a brief introduction for the circumstance of reaction-diffusion systems with constant delays.Examples are given to illustrate the effectiveness of results we get.Then,finite-time synchronization for coupled reaction-diffusion systems with boundary control is considered,including the coupled reaction-diffusion systems with and without delays.For the finite-time synchronization of coupled reaction-diffusion systems without and with time delay,different controllers for Neumann boundary conditions and mixed boundary conditions are studied,respectively.By designing boundary controllers,adequacy criteria that guarantee systems achieve finite-time synchronization are obtained.Examples are given to illustrate the effectiveness of results.At last,finite-time synchronization for adaptive coupled reaction-diffusion systems with pinning control is considered.By using adaptive technique and designing pinning control strategy,adequacy criteria which guarantee systems to achieve finite-time synchronization are obtained.Examples are given to illustrate the effectiveness and correctness of results we get.