Multistability in a three-dimensional oscillator: tori, resonant cycles and chaos

The emergence of multistability in a simple three-dimensional autonomous oscillator is investigated using numerical simulations, calculations of Lyapunov exponents and bifurcation analysis over a broad area of two-dimensional plane of control parameters. Using Neimark–Sacker bifurcation of 1:1 limit...

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Veröffentlicht in:Nonlinear dynamics 2018-12, Vol.94 (4), p.2455-2467
Hauptverfasser: Stankevich, Nataliya, Volkov, Evgeny
Format: Artikel
Sprache:eng
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Zusammenfassung:The emergence of multistability in a simple three-dimensional autonomous oscillator is investigated using numerical simulations, calculations of Lyapunov exponents and bifurcation analysis over a broad area of two-dimensional plane of control parameters. Using Neimark–Sacker bifurcation of 1:1 limit cycle as the starting regime, many parameter islands with the coexisting attractors were detected in the phase diagram, including the coexistence of torus, resonant limit cycles and chaos; and transitions between the regimes were considered in detail. The overlapping between resonant limit cycles of different winding numbers, torus and chaos forms the multistability.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4502-9