On explosion of the chaotic attractor
Abstract
There are presented examples of the rather sudden and violent explosion of the strange attractor of a one-dimensional driven damped anharmonic oscillator induced by a relatively small change of the amplitude of the strongly nonperturbative periodic driving force. A phenomenologic characterization of the explosion of the strange attractor has been given in terms of the behavior of the average maximal Lyapunov exponent ${\bar \lambda}$ and that of the fractal dimension $D_{q}$ for $q=-4$. It is shown that the building up of the exploding strange attractor is accompanied by a nearly linear increase of the maximal average Lyapunov exponent ${\bar \lambda}$. A sudden jump of the fractal dimension $D_{-4}$ is detected when the explosion starts off from an attractor consisting of disjoint bunches separated by an empty phase-space region.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.4843
- arXiv:
- arXiv:1406.4843
- Bibcode:
- 2014arXiv1406.4843B
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 14 pages, 13 figures