Co-Existence of Chaos and Stable Periodic Orbits in a Simple Discrete Neural Network

In designing a neural network for content-addressable memory of spatial patterns, large capacity is desirable. In view of dynamical systems, it requires that the model system for the network have large number of stable (retrievable) periodic solutions. Recently, Wu and Zhang [21] considered the following simple discrete network of two identical neurons with excitatory interactions: { x(n) = βx(n − 1)+ α f (y(n − k)), y(n) = βy(n − 1)+ α f (x(n − k)), (1.1)