Hopf Bifurcation Of A Nonlinear System Derived From Lorenz System Using Centre Manifold Approach

Abstract

A nonlinear system derived from Lorenz system was presented recently by Tee and Salleh (2013a). Although some basics dynamics were presented, the Hopf bifurcation analysis for the system has not been illustrated yet. Thus, the Hopf bifurcation of the system was determined and the directions of the Hopf bifurcation were demonstrated. We discovered the dynamics on centre manifold of the system and the direction of the Hopf bifurcation in more general cases which supports our finding in Tee and Salleh (2013b). The system shows complexity within the system and is worth to be further researched in the future.