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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Li, G.X., Moon, F.C. Fractal basin boundaries in a two-degree-of-freedom nonlinear system. Nonlinear Dyn 1, 209–219 (1990). https://doi.org/10.1007/BF01858294
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DOI: https://doi.org/10.1007/BF01858294