## Periodic solutions for shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales.(English)Zbl 1406.34109

Summary: A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale $$\mathbb T=\mathbb R$$ or $$\mathbb Z$$. Moreover, we present illustrative numerical examples to show the feasibility of our results.

### MSC:

 34N05 Dynamic equations on time scales or measure chains 34C25 Periodic solutions to ordinary differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics
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