Birth of strange nonchaotic attractors due to interior crisis

Abstract We study the interior crisis in the period-3-window of the quasiperiodically forced logistic map. Two routes from quasiperiodicity to chaos involving strange nonchaotic attractors (SNA) are discovered: Along one route we observe a sudden widening of the SNA. This is similar to the interior crisis in chaotic systems. Along the other route we find a direct transition from an invariant curve to a strange nonchaotic attractor exactly at the interior crisis point. This is a new mechanism of the appearance of strange nonchaotic attractors. Beyond the interior crisis the temporal behavior can be described as a crisis-induced intermittency, whose scaling behavior is discussed.

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