Dynamics of anti-periodic solutions on shunting inhibitory cellular neural networks with multi-proportional delays

摘要

Since proportional delay is monotonically increasing, a neural network involving multi-proportional delays is obviously not anti-periodic, yet a very interesting fact in this paper shows that it is possible there is an anti-periodic solution for such systems. This paper aims to deal with the issue of anti-periodic solutions for SICNNs (Shunting Inhibitory Cellular Neural Networks) involving multi-proportional delays. With the help of Lyapunov method, inequality techniques and a concise mathematical analysis proof, sufficient criteria on the existence of anti-periodic solutions including its uniqueness and exponential stability are established. The obtained results provide us some lights for designing a stable SICNNs and complement some earlier publications. Furthermore, simulations show that the theoretical anti-periodic dynamics are in excellent agreement with the numerically observed behavior. (C) 2019 Elsevier B.V. All rights reserved.