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Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms. (English) Zbl 1427.35293

One considers a class of neural networks modeled by partial differential equations with time-varying delays and reaction-diffusion term and the equilibrium in the origin. For particular values of coefficients, one obtains a set of models as for instance: reaction-diffusion static neural network models, reaction-diffusion local field neural network models, delayed reaction-diffusion local field neural networks models or delayed reaction-diffusion static neural network models. The considered general model can be found in an earlier paper of [X. Zhang and Q. Han, “Global asymptotic stability for a class of generalized neural networks with interval time-varying delays”, IEEE Trans. Neural Net. 22, No. 8, 1180–1192 (2011; doi:10.1109/TNN.2011.2147331)]. The synchronization problem is investigated. Dirichlet as well as Neumann boundary conditions are considered. Under special additional assumptions, a delay-derivative dependent and delay-range dependent synchronization criteria is obtained. The conditions depend on neural networks parameter, time delays and diffusion effects. The criteria extends some known results in the domain. Numerical simulations illustrate the mentioned results.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92B20 Neural networks for/in biological studies, artificial life and related topics
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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