Symbolic dynamics and relaxation oscillations |
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Authors: | John Guckenheimer |
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Institution: | Division of Natural Sciences, University of California, Santa Cruz, CA USA |
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Abstract: | This paper describes the application of qualitative methods of dynamical systems theory to a specific problem. It examines the forced Van der Pol equation as an example of a relaxation oscillation with aperiodic solutions. The technique of symbolic dynamics, particularly for one-dimensional mappings, is used to give a complete topological characterization of the set of these aperiodic solutions for parameter values for which the equation appears structurally stable. These results are a mathematical interpretation of numerical computations and are not the result of rigorous analysis. |
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