2000/12/11 by A. Venkatesan, M. Lakshmanan · 52 citations
Computer Science · Mathematics · Physics and Astronomy · #Attractor #Bifurcation #Chaos control and synchronization #Geometry #Intermittency #Lyapunov exponent #Mathematical analysis #Mathematics #Mechanics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Parameter space #Period-doubling bifurcation #Phase space #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Torus #nlin.CD
paper · pdf · doi:10.1103/physreve.63.026219
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 63(2), 026219 (American Physical Society) · 27 pages, RevTeX 4, 16 EPS figures. Phys. Rev. E (2001) to appear
arxiv created 2000/12/11 · openalex publication_date 2001/01/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.