Fractalization route to strange nonchaotic dynamics

Datta, Sandip ; Ramaswamy, Ramakrishna ; Prasad, Awadhesh (2004) Fractalization route to strange nonchaotic dynamics Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 70 (4). Article ID 046203. ISSN 1539-3755

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In the fractalization route for the formation of strange nonchaotic attractors (SNA’s) in quasiperiodically driven nonlinear dynamical systems, a smooth torus gradually becomes a fractal as the forcing amplitude is increased, while the Lyapunov exponent remains nonpositive. Using techniques introduced by Kim et al. to identify unstable sets in SNA’s, we study torus fractalization in a sequence of approximations wherein the quasiperiodic drive is replaced by periodic forcing of increasing period. This allows us to identify an unstable set embedded in the attractor. In the periodically forced system, we show that there is a cascade of attractor merging crises, and argue that the quasiperiodic analogue of such crises causes fractalization of tori to create SNA’s.

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Source:Copyright of this article belongs to The American Physical Society.
ID Code:98867
Deposited On:26 May 2015 12:05
Last Modified:26 May 2015 12:05

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