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Received February 20, 2019; Accepted July 4, 2019; July 30, 2019
Abstract. The purpose of this paper is to propose some formulae for Hopf bifurcation analysis, and investigate applications to a chaotic system. We perform a substantial simplification for the classical Hopf bifurcation formulae. Our results can be extended to multi-dimensional quadratic systems. As an application, we consider the Genesio-Tesi system. Finally, the dynamics of the system are analyzed by bifurcation diagrams, Lyapunov exponents, phase portraits and Poincaré maps. We show that the system can generate chaos via a Hopf bifurcation and period doubling cascade as the control parameter varies. Some other bifurcations can be observed, which includes saddle-node bifurcations, interior crises and boundary crises.
How to Cite this Article:
Bo Sang, Hopf bifurcation formulae and applications to the Genesio-Tesi system, Vol. 2019 (2019), Article ID 34, pp. 1-16