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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Complex dynamics in the Oregonator model with linear delayed feedback.

K Sriram1, S Bernard

  • 1Constraints Project, INRIA, Rocquencourt, BP105, 78153, Le Chesnay Cedex, France. sridelin@yahoo.co.in

Chaos (Woodbury, N.Y.)
|July 8, 2008
PubMed
Summary
This summary is machine-generated.

Delayed feedback in the Belousov-Zhabotinsky reaction, modeled by the Oregonator, generates complex dynamics. This study reveals how delay and canard bifurcations interact to create chaos and mixed-mode oscillations.

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Last Updated: Jul 3, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Published on: September 23, 2025

Area of Science:

  • Chemical Kinetics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • The Belousov-Zhabotinsky (BZ) reaction exhibits complex oscillatory behavior.
  • Delayed feedback is known to significantly alter the dynamics of oscillating systems.

Purpose of the Study:

  • To investigate the complex dynamics arising from linear delayed feedback applied to the Oregonator model of the BZ reaction.
  • To explore the interplay between time delay and canard bifurcations in generating novel dynamical behaviors.

Main Methods:

  • Utilized the Oregonator model for simulating the BZ reaction dynamics.
  • Employed numerical bifurcation continuation and other numerical techniques.
  • Analyzed dynamics in the feedback-delay strength space.
  • Qualitatively explained dynamics using phase portrait projections onto nullclines.

Main Results:

  • Observed a rich variety of complex dynamics including period-doubling to chaos, amplitude death, fractal tori, and mixed-mode oscillations.
  • Identified delay-driven transitions between oscillation amplitudes via canard bifurcations.
  • Found that period-doubling and quasiperiodic routes to chaos occur in a low-dimensional subspace.
  • Demonstrated the generation of chaotic-excitable spikes through ejected chaotic trajectories.

Conclusions:

  • The interaction between time delay and canard bifurcations is a novel mechanism for generating complex dynamics in the BZ reaction.
  • This study provides the first evidence of delay-induced complex dynamics driven by canard bifurcations.
  • The findings offer insights into the fundamental mechanisms underlying chaos and complex oscillations in reaction-diffusion systems.