The limit cycle oscillation can make successive subharmonic bifurcations, until a chaotic state ultimately develops. The Lorenz model is one of the best investigated examples with such behaviour. The transition to a chaotic state is explained by a nonlinear Mathieu equation, which is shown to exhibit successive subharmonic bifurcations. This is our first step in theoretically treating the transition to a chaotic state in a dynamical system.
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Atsushi Ito (1979) studied this question.
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