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Crisis Resonance in Multistable regime

Binoy Krishna Goswami
Autonomous nonlinear systems commonly exhibit simultaneous coexistence, in the phase space, of chaos and stable steady states, created by subcritical Hopf bifurcation. We show that such chaotic instability can be destroyed by small-amplitude modulation of any system parameters. The chaotic attractor undergoes boundary crisis due to modulation-induced collision with an unstable periodic orbit (UPO). Such boundray crisis exhibits a new resonance that we refer to as 'crisis resonance' in the control parameter space. Crisis resonance implies that crisis occurs at minimal modulation depth due to maximal evolutions of the UPOs and the chaotic attractor. Crisis resonance occurs close to some critical frequency (we refer to as `crisis resonance frequency') or its multiples. The UPO frequency is a good estimate of the crisis resonance frequency.
The small-amplitude parameter modulation destroyes chaos in the presence of noise as well. These features are observed theoretically with the paradigm of autonomous systems, namely Lorenz equations of thermal hydraulics and are in excellent agreement with the experimental results, obtained with an analog circuit of Lorenz equations.
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