Theoretical and experimental observation of border-collision bifurcations, coexisting attractors, and complex Arnol’d tongues in a driven piecewise-constant oscillator

Hironobu Kuriyama, Tadashi Tsubone, Munehisa Sekikawa, Naohiko Inaba and Hideaki Okazaki

Chaos, Solitons & Fractals, 2025, vol. 199, issue P1

Abstract: This paper investigates the behavior of one of the simplest Filippov systems, referred to as a piecewise-constant oscillator. We establish both experimentally and numerically that the system exhibits hysteresis behavior characterized by the existence of distinct entrance and exit boundaries of typical Arnol’d tongues. Furthermore, complex bifurcation structures caused by border-collision bifurcations (BCBs) are shown to generate attractors that coexist at a single point in parameter space. In a given parameter space, in the neighborhood of BCBs, it is known that coexisting attractors can be seen. This work presents a novel analytical derivation of successive border-collision fold and pitchfork bifurcation boundaries as well as the experimental observation of distinct exits from and entrances to Arnol’d tongues. These experimental findings were observed in a physically realized oscillator circuit.

Keywords: Border-collision bifurcations; Chaos; Arnol’d tongues; Piecewise-constant oscillator; Coexisting attractors (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006538

DOI: 10.1016/j.chaos.2025.116640

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