Numerical Approach for Local Bifurcation Analysis of Nonlinear Physical System

Abstract

In this paper, we propose an study that combines classical linearization method with the Routh Herwitz criterion theory of complex nonlinear systems to compute local stability boundaries and visualize such bifurcation surfaces of nonlinear dynamical systems as function of parameters set (Analytical Search for Bifurcation Surfaces in Parameter Space). Therefore, we proposed a numerical method for the bifurcation analyses , Our goal is to applied the optimal derivative (based on the minimization in the least-square sense) as introduced by O.Arino and T. Benouaz. In order to gain some progress with this procedure in the term of bifurcation analysis (detection of the local bifurcation in the neighborhood of the bifurcation parameters with respect to an initial condition) . This application enables us to compare the results obtained with those found by the classical linearization (Fréchet derivative (jaccobian matrix) in the equilibriums points)