ROBUST CHAOS IN AUTONOMOUS TIME-DELAY SYSTEM
Cite this article as:
Arzhanukhina D. S., Kuznetsov S. P. ROBUST CHAOS IN AUTONOMOUS TIME-DELAY SYSTEM. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 2, pp. 36-49. DOI: https://doi.org/10.18500/0869-6632-2014-22-2-36-49
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback loops characterized by two generally distinct retarding time parameters. In the case of their equality, chaotic dynamics is associated with the Smale–Williams attractor that corresponds to the double-expanding circle map for the phases of the carrier of the oscillatory trains. Alternatively, at appropriately chosen two different delays attractor is close to torus with Anosov dynamics on it as the phases are governed by the Fibonacci map. In both cases the attractors manifest robustness (absence of regularity windows under variation of parameters) and presumably relate to the class of structurally stable hyperbolic attractors.
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BibTeX
author = {D. S. Arzhanukhina and Sergey P. Kuznetsov},
title = {ROBUST CHAOS IN AUTONOMOUS TIME-DELAY SYSTEM},
year = {2014},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {22},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/robust-chaos-in-autonomous-time-delay-system},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2014-22-2-36-49},pages = {36--49},issn = {0869-6632},
keywords = {Attractor,hyperbolic chaos,maps,Anosov dynamics,Arnold cat,Fibonacci map,Smale–Williams attractor.},
abstract = {We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback loops characterized by two generally distinct retarding time parameters. In the case of their equality, chaotic dynamics is associated with the Smale–Williams attractor that corresponds to the double-expanding circle map for the phases of the carrier of the oscillatory trains. Alternatively, at appropriately chosen two different delays attractor is close to torus with Anosov dynamics on it as the phases are governed by the Fibonacci map. In both cases the attractors manifest robustness (absence of regularity windows under variation of parameters) and presumably relate to the class of structurally stable hyperbolic attractors. }}