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Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms. (English) Zbl 1199.39006

Summary: An impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms is considered.
The reaction-diffusion terms are approximated by divided differences. For simplicity of notation, the spatial domain \(\Omega\) is assumed to be a finite closed interval \([a,b]\). Under suitable conditions in terms of \(M\)-matrices it is proved that the system obtained has a unique equilibrium point which is globally exponentially stable.

MSC:

39A12 Discrete version of topics in analysis
92B20 Neural networks for/in biological studies, artificial life and related topics
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
39A30 Stability theory for difference equations
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