A Qualitative Study of Solutions of Nonlinear Coupled Ordinary Differential Equations

Abstract

There are many physical phenomena where systems of differential equations are newlineused to model the situation. The prey-predator model of mathematical ecology, newlinedouble pendulum, flow in magneto hydrodynamics, non-linear optics to name a newlinefew. A system of Ordinary Differential Equations (ODEs) is called Coupled Ordinary Differential Equations (CODE) where simultaneous Differential Equations are newlinedefined on the same interval and the dependent variables in each of these equations newlineare from the same set of variables. The literature containing qualitative study of newlineODEs is vast. To the best of our knowledge, not much work is done specific to the newlineCODEs. This work for the Ph.D. Thesis is towards developing a comprehensive newlinequalitative theory of CODEs. We use Functional Analytic Techniques and Fixed newlinePoint theory, in particular. This work includes a study of qualitative behaviour newlineof solutions of systems of non-linear CODE. newline