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Guckenheimer, J. and Holmes, P. (1997) Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York.

has been cited by the following article:

• TITLE: Bifurcations and Chaos in the Duffing Equation with One Degenerate Saddle Point and Single External Forcing

  AUTHORS: Zhiyang Yang, Tao Jiang

  KEYWORDS: Duffing Equation, Melnikov Method, Numerical Simulations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.9, October 16, 2017

  ABSTRACT: In this paper, we study the Duffing equation with one degenerate saddle point and one external forcing and obtain the criteria of chaos of Duffing equation under periodic perturbation through Melnikov method. Numerical simulations not only show the correctness of the theoretical analysis but also exhibit the more new complex dynamical behaviors, including homoclinic bifurcation, bifurcation diagrams, maximum Lyapunov exponents diagrams, phase portraits and Poincaré maps.