Reply to ‘ ‘ Comment on ‘ Intermittency in chaotic rotations ’ ’ ’
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چکیده
Intermittency and chaotic rotations are interesting recent topics in nonlinear dynamics, and we are pleased that our contribution @2# is of sufficient interest to have generated the preceding Comment by Pikovsky and Rosenblum @1#. We welcome the opportunity to respond and to clarify our work. The main point of our original paper is that a chaotic rotation typically exhibits an intermittent behavior @2#. The physical intuition for our study comes from the observation of rotational structures in well studied chaotic flows such as the Rössler oscillator @3#. The differential equations of the Rössler system apparently contain an ideal rotational structure generated by a harmonic oscillator, as follows:
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Comment on "Intermittency in chaotic rotations".
Lai et al. [Phys. Rev. E 62, R29 (2000)] claim that the angular velocity of the phase point moving along the chaotic trajectory in a properly chosen projection (the instantaneous frequency) is intermittent. Using the same examples, namely the Rössler and the Lorenz systems, we show the absence of intermittency in the dynamics of the instantaneous frequency. This is confirmed by demonstrating th...
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We examine the rotational dynamics associated with bounded chaotic flows, such as those on chaotic attractors, and find that the dynamics typically exhibits on-off intermittency. In particular, a properly defined chaotic rotation tends to follow, approximately, the phase-space rotation of a harmonic oscillator with occasional bursts away from this nearly uniform rotation. The intermittent behav...
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