Introducing the Analysis of Bifurcation in Dynamical Systems by Symbolic Computation

Abstract

The aim of this paper is to introduce a few topics about nonlinear systems that are usual in electrical engineering but are frequently disregarded in undergraduate courses. More precisely, the main subject of this paper is to present the analysis of bifurcations in dynamical systems through the use of symbolic computation. The necessary conditions for the occurrence of Hopf, saddle-node, transcritical or pitchfork bifurcations in first order state space nonlinear equations depending upon a vector of parameters are expressed in terms of symbolic computation. With symbolic computation, the relationship between the state variables and the parameters that play a crucial role in the occurrence of such phenomena can be established. Firstly, the symbolic computation is applied to a third order dynamic Lorenz system in order to familiarise the students with the technique. Then, the symbolic routines are used in the analysis of the simplified model of a power system, bringing new insights and a deeper understanding about the occurrence of these phenomena in physical systems.