Analysis of discrete time competitive-cooperative neural networks

Discrete time competitive-cooperative neural networks are investigated using a decomposition approach that embeds a competitive-cooperative neural network into an augmented cooperative system by splitting the synaptic weights into inhibitory and excitatory groups. This allows for the use of the basic order-preserving property of cooperative systems to study the original network system. Properties such as quasi-ordering, positive invariance, dissipativity, convergence, and stability of the networks are analyzed, yielding detailed characterization of the system trajectory bounds and decay rates. A simple yet effective procedure is also proposed for the design of a network with prescribed equilibria and guaranteed basin of attraction and decay rate.