A unified treatment for stability preservation in computer simulations of impulsive BAM networks

This paper is concerned with the stability preservation in computer simulations of an impulsive bidirectional associative memory (BAM) network. The simulations are provided by difference equations formulated from a semi-discretisation technique and impulsive maps as discrete-time representations of the nonlinear impulses which attempt to destabilise the BAM network at fixed moments of time. Prior to producing the computer simulations, the analogue is analysed for its exponential convergence towards a unique equilibrium state. The analysis exploits the method of Lyapunov sequences to derive several sufficient conditions that govern the network parameters and the impulse magnitude and frequency. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. The treatment of the analysis leads us to a relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals.