Abstract
In this chapter, we consider some of the most broadly applicable techniques for the analysis of discrete and continuous time dynamical systems such as Eigenvalue Methods and Phase Portraits. These methods can provide important qualitative information about the behavior of dynamical systems, even when exact analytic solutions are not obtainable. Eigenvalue method is used to analyze nonlinear dynamical systems for stability and is an appropriate application for a computer algebra system. Its methods can be applied to both continuous time dynamical systems and discrete time dynamical systems. The same concept can be used to obtain the phase portrait, which is a graphical description of the dynamics over the entire state space. A phase portrait is mapped by homeomorphism, a continuous function with a continuous inverse.
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