This study examines finite-time synchronization for a class of N-coupled complex partial differential systems (PDSs) with time-varying delay. The problem of finite-time synchronization for coupled drive-response PDSs with timevarying delay is similarly considered. The synchronization error dynamic of the PDSs is defined in the q-dimensional spatial domain. We construct a feedback controller to achieve finite-time synchronization. Sufficient conditions are derived by using the Lyapunov-Krasoviskii stability approach and inequalities technology to ensure that the proposed networks achieve synchronization in finite time. The proposed systems demonstrate extensive application. Finally, an example is used to verify the theoretical results.
With Poincare's inequality and auxiliary function applied in a class of retarded cellular neural networks with reaction-diffusion, the conditions of the systems' W 1,2 (Ω )-exponential and X 1,2 (Ω )-asmptotic stability are obtained. The stability conditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end. cellular neural networks, reaction-diffusion, W
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