A numerical study on iso-spiking bifurcations of some neural systems

Abstract

Many biological systems can be usefully simulated by mathematical models involving dynamical systems. These models will exhibit spike-like phenomenon through a series of bursts. If a system has a constant integer spike number (the number of spikes per burst) for all bursts, the system is said to be iso-spiking. Using the spike number as a neural discretization analog for stimulatory parameters in the iso-spiking region and deriving scaling laws for this neural encoding scheme (as applied to the dynamical system) we show that the natural number 1 is a universal number depending only on the encoding scheme. Computer simulations are presented to support the theorectical predictions.