Mathematical Catastrophe with Applications

In this paper, we have studied the nerve impulse (action potential impulse), and amplitude of the nerve impulse, and then we attempt to fit a catastrophic model for the differential equation which represents the Nerve cell behavior specially excitation of the nerve cell and its catastrophic phenomena by methods of catastrophe theory. The main aim of this paper is to find a catastrophe model to represent the catastrophic behavior of nerve cells, and we have shown that there is a catastrophic behavior of the nerve cell and that there is a mathematical model to represent a Nerve Cell behavior. Furthermore, Nerve behavior is of Cusp type Catastrophe.