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Traveling echo waves in an array of excitable elements with time-delayed coupling.

Oriol Vallès-Codina1, Ronny Möbius, Sten Rüdiger

  • 1IBE-Institut de Biologia Evolutiva (UPF/CSIC), Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 27, 2011
PubMed
Summary
This summary is machine-generated.

Time-delayed coupling in FitzHugh-Nagumo elements creates complex spike dynamics, including splitting, echoes, and antiphase synchronization. These effects depend on the delay time, influencing pulse characteristics and system stability.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Complex systems

Background:

  • Excitable media, like the FitzHugh-Nagumo model, are fundamental to understanding phenomena such as signal propagation in biological systems.
  • Time delays in coupling are common in real-world systems and can significantly alter dynamics.

Purpose of the Study:

  • To investigate the impact of time-delayed excitatory coupling on one-dimensional arrays of discrete FitzHugh-Nagumo elements.
  • To characterize the emergent behaviors and bifurcations induced by varying time delays.

Main Methods:

  • Numerical simulations of one-dimensional arrays of FitzHugh-Nagumo elements.
  • Analysis of spike prolongation, splitting, echo effects, and synchronization patterns.
  • Characterization of pulse speed, duration, and bifurcations to stationary regimes.

Main Results:

  • Small time delays prolong noise-triggered spikes.
  • Larger delays induce spike splitting and damped series of spikes (echo effect).
  • Very large delays lead to antiphase synchronization and a transition to a stationary regime.

Conclusions:

  • Time-delayed coupling introduces rich dynamical behaviors in excitable media.
  • The system exhibits transitions from simple spike modification to complex synchronized states based on delay duration.
  • Understanding these dynamics is crucial for modeling coupled biological and physical systems.