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Hopf Bifurcation of a Nonlinear System Derived from Lorenz System Using Normal Form Theory

Z. Salleh, L. S. Tee

Abstract



A dynamical system has been studied intensively in recent years by many mathematicians. A simple dynamical system may exhibit complex behaviour such as periodic orbit, bifurcations and chaos. Hopf bifurcation is one of such behavioural in bifurcations that has been studied. However, researchers preferred to find the direction of Hopf bifurcation in a very specific example. This paper presents an extensive analysis of the dynamical system regarding the direction of the Hopf bifurcation using the normal form theory. The detail calculations were presented and the results showed that the system displays a strong complexity. The conditions for supercritical and subcritical were demonstrated in a general case which agrees with our previous findings.

Keywords


Dynamical system, Hopf bifurcation, centre manifold theorem, normal form theory.

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