Computer simulations of exponentially convergent networks with large impulses

This paper demonstrates the use of a semi-discretization technique for obtaining a discrete-time analogue of an exponentially convergent network that is subject to impulses with large magnitude. Prior to implementing the analogue for computer simulations, we investigate its exponential convergence towards a unique equilibrium state and thereby obtain a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency. Although the time-step does not appear in the conditions that govern the network parameters, its value needs to be sufficiently small in order for the analogue displays correct convergence behaviour of the network when subjected particularly to large impulses.