Catastrophe theory

Abstract

The catastrophe theory, to study the non-linear differential system, as enunciated by Thom is discussed. Seven elementary catastrophes according to the classifications made by earlier authors are presented here, Increasing the order of non-linearity of the Duffing's equations we have studied the equation x. + 2 lx + X + a x3+bx5 = o cos n t. The catastrophe manifold in this case is butterfly catastrophe. The Duffing's equation is also discussed as a model to study the dynamics of brain used earlier by Zeeman, The differential equation for heart beat and nerve impulse given by Zeeman are also discussed in this paper, The controversies regarding catastrophe theory and its variety of applications are summarized.