Successive bifurcations leading to stochastic behavior
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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.
Key wordsBifurcation correlation function dissipative nonlinear nonperiodic normal mode quasiperiodic stochastic turbulence
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