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Strange nonchaotic attractors in driven excitable systems.

Awadhesh Prasad1, Bibudhananda Biswal, Ramakrishna Ramaswamy

  • 1Department of Bioengineering, Arizona State University, Tempe, Arizona 85287, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

Quasiperiodic forcing drives excitable systems into stable, aperiodic spiking. This phenomenon arises from strange nonchaotic dynamics, characterized by fractal attractors and negative largest Lyapunov exponents.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Excitable systems exhibit threshold dynamics.
  • Quasiperiodic forcing introduces complex temporal patterns.
  • Understanding stability in driven nonlinear systems is crucial.

Purpose of the Study:

  • To investigate the dynamics of excitable systems under quasiperiodic forcing.
  • To identify conditions leading to stable, aperiodic spiking behavior.
  • To characterize the underlying dynamical mechanisms.

Main Methods:

  • Numerical simulations of a model excitable system.
  • Application of quasiperiodic forcing functions.
  • Analysis of time series data for spiking patterns.
  • Calculation of Lyapunov exponents to assess dynamics.

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Main Results:

  • Stable, aperiodic spiking was achieved in the excitable system.
  • The system's dynamics were shown to reside on a fractal attractor.
  • A negative largest Lyapunov exponent confirmed nonchaotic behavior.

Conclusions:

  • Quasiperiodic forcing can stabilize complex dynamics in excitable systems.
  • Strange nonchaotic dynamics provide a framework for understanding this behavior.
  • The findings offer insights into controlling and predicting responses in nonlinear systems.