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Existence and global exponential stability of periodic solution of CNNs with impulses. (English) Zbl 1148.34045

Sufficient conditions are obtained for the existence and global stability of a periodic solution of the following impulsive system \[ \frac{dx_i}{dt}=-a_i(t)x_i(t)+\sum_{j=1}^n [b_{ij}(t)f_j(x_j(t))+c_{ij}(t)f_j(x_j(t-\tau_j(t)))]+I_i(t),~ t\geq 0, t\not= t_k, \]
\[ \Delta x_i(t_k)=-\gamma_{ik}x_i(t_k). \] For the existence result the authors apply Mawhin’s continuation theorem of coincidence degree theory.

MSC:

34K13 Periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
47N20 Applications of operator theory to differential and integral equations
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References:

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