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JOURNALS // Izvestiya VUZ. Applied Nonlinear Dynamics // Archive

Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, Volume 22, Issue 2, Pages 36–49 (Mi ivp228)

DETERMINISTIC CHAOS

Robust chaos in autonomous time-delay system

Arzhanukhinaa, S. P. Kuznetsovbc

a Saratov State University
b Saratov Branch, Kotel'nikov Institute of Radio-Engineering and Electronics, Russian Academy of Sciences
c University of Potsdam

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.

Keywords: Attractor, hyperbolic chaos, maps, Anosov dynamics, Arnold cat, Fibonacci map, Smale-Williams attractor.

UDC: 517.929:621.373

Received: 17.03.2014

Language: English



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