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.