Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map: mechanisms and their characterizations

Venkatesan, A. ; Lakshmanan, M. (2001) Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map: mechanisms and their characterizations Physical Review E, 63 (2). 026219_1-026219_14. ISSN 1063-651X

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Official URL: http://link.aps.org/doi/10.1103/PhysRevE.63.026219

Related URL: http://dx.doi.org/10.1103/PhysRevE.63.026219

Abstract

A simple quasiperiodically forced one-dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors (SNAs) in a two-parameter (A-f) space. The routes include transitions to chaos via SNAs from both a one-frequency torus and a period-doubled torus. In the former case, we identify the fractalization and type-I intermittency routes. In the latter case, we point out that at least four distinct routes for the truncation of the torus-doubling bifurcation and the creation of SNAs occur in this model. In particular, the formation of SNAs through Heagy-Hammel, fractalization, and type-III intermittent mechanisms is described. In addition, it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor, which tames the growth of period-doubling bifurcation, takes place, creating the SNA. The SNAs created through different mechanisms are characterized by the behavior of the Lyapunov exponents and their variance, by the estimation of the phase sensitivity exponent, and through the distribution of finite-time Lyapunov exponents.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:19438
Deposited On:22 Nov 2010 12:36
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