Multiperiodicity and Exponential Attractivity of Neural Networks with Mixed Delays

This paper studies the multiperiodicity and exponential attractivity evoked by periodic external inputs in cellular neural networks with discrete delays and distributed delays. We show that an n-neuron cellular neural network with mixed delays can have 2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^n$$\end{document} periodic orbits located in saturation regions and these periodic orbits are locally exponentially attractive. Besides, some conditions for ascertaining periodic orbits to be locally exponentially attractive and allowing them to locate in any designated region are derived. The simulation results show that the proposed results are effective.