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Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays. (English) Zbl 1221.34167

Summary: A class of Cohen-Grossberg neural networks with bounded and unbounded delays is considered. We establish some sufficient conditions on the existence and exponential stability of anti-periodic solutions for the following Cohen-Grossberg neural networks:

x i ' (t)=-a i (x i (t))[b i (x i (t))- j=1 n c ij (t)f j (x j (t))- j=1 n d ij (t)g j (x j (t-τ ij (t)))- j=1 n e ij (t) 0 k ij (θ)h j (x j (t-θ))dθ-I i (t)],

i=1,2,,n· We also present an example to illustrate the feasibility and effectiveness of our results.

MSC:
34K05General theory of functional-differential equations
34K20Stability theory of functional-differential equations
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)
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