Fractal basin boundaries in a two-degree-of-freedom nonlinear system |
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| Authors: | G X Li F C Moon |
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| Institution: | (1) Sibley School of Mechanical and Aerospace Engineering, Cornell University, 14853 Ithaca, NY, USA;(2) Present address: Department of Mechanical Engineering, McGill University, Montreal, Québec, Canada;(3) Present address: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York |
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| Abstract: | The final state for nonlinear systems with multiple attractors may become unpredictable as a result of homoclinic or heteroclinic bifurcations. The fractal basin boundaries due to such bifurcations for a four-well, two-degree-of-freedom, nonlinear oscillator under sinusoidal forcing have been studied, based on a theory of homoclinic bifurcation inn-dimensional vector space developed by Palmer. Numerical simulation is used as a means of demonstrating the consequences of the system dynamics when the bifurcations occur, and it is shown that the basin boundaries in the configuration space (x, y) become fractal near the critical value of the heteroclinic bifurcations. |
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| Keywords: | Homoclinic and heteroclinic orbits bifurcation and chaos fractal basin boundaries |
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