Existence and Exponential Stability of Anti-periodic Solutions of High-order Hopfield Neural Networks with Delays on Time Scales

Abstract

On time scales, a class of delayed high-order Hopfield neural networks are considered. We establish some sufficient conditions on the existence and exponential stability of anti-periodic solutions for the following Hopfield neural networks with time-varying and distributed delays $$\begin{array}{l} x_i^{\Delta}(t)\,=\,-c_i(t)x_i(t)+\sum\limits^n_{j=1}a_{ij}(t)f_j\left(x_j(t-\gamma_{ij}(t))\right)\\ \,\quad\,\quad\,\quad\,\,+\,\sum\limits^n_{j=1} \sum\limits_{l=1}^{n}b_{ijl}(t)\int\limits_0^{\infty}k_{ij}(\theta)g_j(x_j(t-\theta))\Delta \theta \int\limits_0^{\infty}k_{il}(\theta)g_l(x_l(t-\theta))\Delta \theta\\ \,\quad\,\quad\,\quad\,\,+\,\quad I_i(t),\quad i=1,2,\ldots,n\end{array}$$ on time scales. Finally, an example is given to show the effectiveness of the proposed method and results.