Stability preserving NSFD scheme for a cooperative and supportive network

A continuous dynamical system of a Cooperative Supportive Neural Network is discretized using Non-Standard Finite Difference scheme. Results in the direction of the existence of equilibria, sufficient conditions for local and global stability of equilibrium are established for the discrete form of the network. Results are compared with those of the continuous model. Theoretical numerical examples with simulations are provided to understand the results. Our study establishes that the Non-Standard Finite Difference scheme chosen here preserves the properties of the continuous system for any step size. Also, the input-output relations of difference equation model are tested using a recently developed technique. Our study is the first of its kind in this area of neural networks.