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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
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Laminar chaos in systems with quasiperiodic delay.
David Müller-Bender1, Günter Radons1,2
1Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.
Physical Review. E
|February 17, 2023
Summary
This study reveals laminar chaos in systems with quasiperiodic delay, where phase durations vary quasiperiodically. This finding offers a novel method for reducing chaotic attractor dimensions in dynamical systems.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Nonlinear Dynamics
Background:
- Laminar chaos, characterized by stable phases interrupted by chaotic bursts, was previously identified in systems with periodic time-varying delay.
- The intensity levels within these laminar phases exhibit chaotic variations between phases.
Purpose of the Study:
- To investigate the occurrence of laminar chaos in dynamical systems with quasiperiodic delay.
- To generalize the concepts of conservative and dissipative delays for quasiperiodic systems.
- To analyze the impact of quasiperiodic delay on chaotic attractor dimensions.
Main Methods:
- Generalization of conservative and dissipative delay concepts to quasiperiodic systems.
- Theoretical analysis of time-delay systems with quasiperiodic modulation.
- Numerical simulations to observe and quantify laminar chaos and attractor dimensions.
Main Results:
- Laminar chaos is demonstrated in systems with quasiperiodic delay.
- Laminar phase durations exhibit quasiperiodic variations, following torus map dynamics.
- Quasiperiodic delay modulation significantly reduces the dimension of chaotic attractors.
- Kaplan-Yorke dimension is quasiperiodically modulated, leading to switches between high- and low-dimensional chaos.
Conclusions:
- Quasiperiodic delay offers a new route to control chaos and reduce attractor dimensions in time-delay systems.
- The observed quasiperiodic modulation of dynamics provides insights into complex system behavior.
- This research expands the understanding of laminar chaos beyond periodic delay systems.
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