Dynamical Systems

Introduction

One of the characteristics of dynamical non-linear systems is their ability to have a drastic changes in their dynamical behavior. In the previous section we have introduced the phase space and characterize the stability of the dynamical systems using the bifurcation diagram in which the fixed points are functions of the parameters. The stability of the system is represented in this diagram by a solid line and unstable fixed points are represented by dashed line. We can found in literature four basic types of bifurcations, we shall discuss some of them in the following.

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