Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2004-11, Vol.70 (5 Pt 2), p.056202-056202, Article 056202
Main Authors: Juárez, L Héctor, Kantz, Holger, Martínez, Oscar, Ramos, Eduardo, Rechtman, Raúl
Format: Article
Language:English
Subjects:
Adaptation, Physiological - physiology
Biological Clocks
Computer Simulation
Models, Biological
Nonlinear Dynamics
Periodicity
Pulsatile Flow - physiology
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Summary:We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of epsilon-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.70.056202