Quasi-Periodic Bifurcations and Chaos

Taoufik Bakri and Ferdinand Verhulst ()
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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

Mathematics, 2025, vol. 13, issue 12, 1-27

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.

Keywords: quasi-periodicity; bifurcation; tori; chaos; Lyapunov exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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