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The global bifurcation and chaos are investigated in this paper for a van der Pol-Duff-ing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The au-tonomous system corresponding to the system under discussion is analytically studied to draw all globalbifureation diagrams in every parameter space, These diagrams are called basic bifurcation ones. Thenfixing parameter in every space and taking the parametrically excited amplitude as a bifurcation param-eter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of nu-merical methods. The results are sufficient to show that the system has distinct dynamic behavior, Fi-nally, the properties of the basins of attraction are observed and the appearance of fractal basin bound-aries heralding the onset of a loss of structural integrity is noted in order to consider how to control theextent and the rate of the erosion in the next paper.
The global bifurcation and chaos are investigated in this paper for a van der Pol-Duff-ing-Mathieu system with a single-and-well potential oscillator by means of nonlinear dynamics. The au-tonomous system corresponding to the system under discussion is analytically studied to draw all globalbifureation diagrams in every parameter space, These diagrams are called basic bifurcation ones. Thenfixing parameter in every space and taking the parametrically excited amplitude as a bifurcation param-eter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of nu-merical methods. The results are sufficient to show that the system has distinct dynamic behavior, Fi-nally, the properties of the basins of attraction are observed and the appearance of fractal basin bound-aries heralding the onset of a loss of structural integrity is noted in order to consider how to control the content and the rate of the erosion in the next paper.