Multiperiodicity and attractivity analysis for a class of high-order Cohen-Grossberg neural networks

In this paper, the multiperiodicity of a class of high-order Cohen-Grossberg neural networks (HOCGNNs) with special activation functions is discussed by using analysis approach and decomposition of state space. The activation functions of this class of neural networks consist of nondecreasing functions with saturation, standard activation functions of cellular neural networks, etc. It is shown that the n-neuron HOCGNNs can have 2ⁿ locally exponentially attractive periodic orbits located in saturation regions. In addition, a condition is derived for ascertaining the periodic orbit to be locally exponentially attractive and to be located in any designated region. Finally, an example is given to show the effectiveness of the obtained results.