The influence of delay time on the generation of chaotic oscillations in a two-dimensional resonant system

Marek Berezowski

Chaos, Solitons & Fractals, 2026, vol. 208, issue P1

Abstract: This paper investigates the influence of time delay on the generation of chaotic oscillations in a two-dimensional resonant system. Extending the methodology presented in Berezowski (2001), a delay is introduced into a resonant differential equation, bridging the classical logistic map with continuous-time oscillatory dynamics. Analytical derivation of characteristic equations allows precise determination of stability boundaries and oscillation frequencies. The oscillation frequency is shown to be independent of the bifurcation parameter, while the onset of instability depends critically on the delay and damping. Numerical simulations, illustrated with Feigenbaum diagrams, reveal period-doubling bifurcations, chaotic regimes, and crises under variations of bifurcation parameter, delay time, damping, and system inertia. The results confirm that delay can serve as a principal mechanism for chaos generation in continuous resonant systems and provide a framework for predicting complex dynamical behavior in physical and engineering applications.

Keywords: Dynamics; Chaos; Equilibrium point; Oscillations; Delay time; Logistic map; Resonance (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002997

DOI: 10.1016/j.chaos.2026.118158

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