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Antipersistent random walks in time-delayed systems.

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Chaotic diffusion in time-delayed systems is modeled using antipersistent random walks. The study reveals how nonlinearity and delay affect diffusion, linking it to Markov processes.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Time-delayed systems exhibit complex behaviors, including chaotic diffusion.
  • Understanding these dynamics is crucial for various scientific fields.
  • Previous models often simplified the interplay of instantaneous and delayed terms.

Purpose of the Study:

  • To model chaotic diffusion in time-delayed systems using a novel approach.
  • To investigate the influence of nonlinearity and delay strength on diffusion characteristics.
  • To connect the observed diffusion patterns to established stochastic processes.

Main Methods:

  • Numerical simulations of time-delayed systems.
  • Analysis using antipersistent random walk models.
  • Analytical derivations to support numerical findings.

Main Results:

  • Chaotic diffusion in these systems is accurately described by antipersistent random walks.
  • Key random walk quantities show clear dependence on nonlinearity and delay.
  • Diffusion coefficient behavior aligns with increasing-order Markov processes as nonlinearity decreases.

Conclusions:

  • Antipersistent random walks provide a robust framework for understanding chaotic diffusion in time-delayed systems.
  • The findings offer insights into the role of nonlinearity and delay in complex system dynamics.
  • This work bridges the gap between deterministic delayed systems and stochastic process descriptions.