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Resonant Doppler effect in systems with variable delay.

D Müller-Bender1, A Otto1, G Radons1

  • 1Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.

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|July 23, 2019
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Summary
This summary is machine-generated.

Time-varying delays in nonlinear systems create novel dynamics, akin to a Doppler effect. Resonant effects yield distinct low- and high-frequency phases, enabling new system designs.

Keywords:
Doppler effectchaosdelay differential equationnonlinear dynamicstime-multiplexingvariable delay

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Delay Systems

Background:

  • Systems with constant delays exhibit limited dynamical behaviors.
  • Time-varying delays introduce complexities not seen in static systems.

Purpose of the Study:

  • To explore the rich dynamical behaviors arising from time-varying delays in nonlinear systems.
  • To analyze the analogy between delay variation and the Doppler effect with self-feedback.
  • To investigate generalized laminar chaos and its orders in dissipative delay systems.

Main Methods:

  • Analysis of nonlinear systems with time-varying delays.
  • Distinguishing between non-resonant (conservative delays) and resonant (dissipative delays) Doppler effects.
  • Systematic study of chaotic dynamics and derivation of criteria for generalized laminar chaos orders.

Main Results:

  • Time-varying delays induce a Doppler effect, leading to quasi-periodic frequency modulation (non-resonant) or distinct low/high-frequency phases (resonant).
  • Resonant effects enable time-multiplexed dynamics, facilitating multistable solutions and temporal switching between dynamics.
  • Generalized laminar chaos is identified in dissipative systems, with orders related to attractor dimension; zeroth-order exhibits low-dimension plateaus.

Conclusions:

  • Time-varying delays significantly expand the dynamical repertoire of nonlinear systems.
  • The resonant Doppler effect offers novel pathways for designing systems with controlled multistability and switching behaviors.
  • Generalized laminar chaos provides a new framework for understanding low-dimensional chaos in delay systems.