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Related Experiment Videos

Basin bifurcations in quasiperiodically forced coupled systems.

Manish Dev Shrimali1, Awadhesh Prasad, Ram Ramaswamy

  • 1Department of Physics, Dayanand College, Ajmer 305 001, India and School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

Quasiperiodic forcing on coupled logistic maps reveals complex dynamics. Parameter changes cause abrupt shifts in attractor basins, creating holes and islands, offering insights into system behavior.

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Area of Science:

  • Complex systems dynamics
  • Nonlinear dynamics
  • Chaos theory

Background:

  • Coupled logistic maps are fundamental models for studying nonlinear dynamics.
  • Quasiperiodic forcing introduces complex temporal variations into dynamical systems.
  • Understanding bifurcations and attractor basin changes is crucial for predicting system behavior.

Purpose of the Study:

  • To investigate the impact of quasiperiodic forcing on coupled identical logistic maps.
  • To characterize the diverse dynamical regimes, including bistability and multistability, that emerge.
  • To analyze the bifurcations of attractor basins within these regimes.

Main Methods:

  • Numerical simulations of coupled logistic map systems.
  • Analysis of system parameter variations.

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  • Examination of attractor basin structures and critical surfaces.

    • Main Results:

    • Observed a variety of dynamical regimes, including bistability and multistability.
    • Identified abrupt changes in attractor basin sizes at the bifurcation to bistability.
    • Documented the creation of holes and islands within attractor basins due to parameter changes.

    Conclusions:

    • Quasiperiodic forcing leads to rich and complex dynamics in coupled logistic maps.
    • Attractor basin bifurcations, including hole and island formation, are key phenomena in bistable regions.
    • Critical surface analysis provides a framework for understanding these complex basin structures.