![]() Eventually the system gets far enough away from the periodic orbit to be affected by chaotic dynamics in the rest of the state space, until it gets close to the orbit again and returns to the nearly periodic behaviour. In the apparently periodic phases the behaviour is only nearly periodic, slowly drifting away from an unstable periodic orbit. ![]() These (type I, II and III) correspond to the approach to a saddle-node bifurcation, a subcritical Hopf bifurcation, or an inverse period-doubling bifurcation. Pomeau and Manneville described three routes to intermittency where a nearly periodic system shows irregularly spaced bursts of chaos. ![]() In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency). This is an example of Pomeau–Manneville dynamics. The system spends long periods close to the bright periodic orbit, occasionally moving away for phases of chaotic dynamics that cover the rest of the attractor.
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