ABSTRACT
In the 19th and early 20th centuries most mathematical models for physical phenomena used linear differential equations which can be solved by analytic techniques. With the rapid advancement of science and engineering and the advent of computers, it was found advantageous to consider sophisticated models where nonlinearities and their impact cannot be ignored. Stability theory addresses the issue of model nonlinearities by making the observation that in many models an initial state of the system will evolve into a steady state. Since most mathematical models provide only an approximation to reality, a basic issue about the steady states is their "response" to "deviations" or perturbations of the system from the steady state. Mathematical models which lead to systems of first order ordinary differential equations appear in many applications. It should be observed also that when sati sodel equations contain second or higher order differential equations, then these equations can be rewritten as a system of first order equations.
