System Of Non-linear Ordinary Differential Equations And Stability Analysis

The focus of this thesis is on the use of linearization techniques and linear differential equation theory to analyze nonlinear differential equations. Often, mathematical models of real-world phenomena are formulated in terms of systems of nonlinear differential equations, which may be difficult to solve explicitly. To overcome this barrier, we take a qualitative approach to the analysis of solutions to nonlinear systems by making phase portraits and using stability analysis. We demonstrate these techniques in the analysis of two systems of nonlinear differential equations. The first part of this paper gives a survey of standard linearization techniques in ordinary differential equation theory. The second part of the paper presents applications of these techniques to particular systems of nonlinear ordinary differential equation.

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