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Quasi-Periodic Bifurcations and Chaos

Author

Listed:
  • Taoufik Bakri

    (TNO Sustainable Urban Mobility & Safety, P.O. Box 96800, 2509 JE The Hague, The Netherlands)

  • Ferdinand Verhulst

    (Mathematisch Instituut, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands)

Abstract

A natural phenomenon in applications is the interaction of quasi-periodic solutions of dynamical systems in a dissipative setting. We study the interactions of two of such ODE systems based on the construction of a nonlinear oscillator with thermostatic (energy) control. This leads to the emergence of complexity, torus doubling, and chaos. We find canards; 1-, 2-, and 3-tori; chaos, and hyperchaos. Detailed analysis is possible in the case of small oscillations and small interactions. Large-scale phenomena are studied by the construction of charts of parameter space using Lyapunov exponents.

Suggested Citation

  • Taoufik Bakri & Ferdinand Verhulst, 2025. "Quasi-Periodic Bifurcations and Chaos," Mathematics, MDPI, vol. 13(12), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1940-:d:1676392
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