Abstract
A model of interacting normal modes in a nonlinear, dissipative system is constructed in order to analyze speculations by Ruelle and Takens. The first bifurcation leads to a periodic state. The second bifurcation leads to phaselocking, if the first mode is sufficiently energetic. A third bifurcation leads to stochastic behavior. Possible relevance of these phenomena for physical systems is discussed.
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McLaughlin, J. Successive bifurcations leading to stochastic behavior. J Stat Phys 15, 307–326 (1976). https://doi.org/10.1007/BF01023056
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DOI: https://doi.org/10.1007/BF01023056