TY - JOUR

T1 - Multistability in a three-dimensional oscillator

T2 - tori, resonant cycles and chaos

AU - Stankevich, Nataliya

AU - Volkov, Evgeny

N1 - Publisher Copyright: © 2018, Springer Nature B.V.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Bifurcation analysis

KW - Chaos

KW - Lyapunov exponents

KW - Multistability

KW - Quasiperiodic oscillations

UR - http://www.scopus.com/inward/record.url?scp=85051224370&partnerID=8YFLogxK

U2 - 10.1007/s11071-018-4502-9

DO - 10.1007/s11071-018-4502-9

M3 - Article

AN - SCOPUS:85051224370

VL - 94

SP - 2455

EP - 2467

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -