Periodic bursting behaviors induced by pulse-shaped explosion or non-pulse-shaped explosion in a van der Pol-Mathieu oscillator with external excitation

DOI10.1016/j.cnsns.2021.105959zbMath1482.34113OpenAlexW3181055709MaRDI QIDQ2246956

Yue Yu, Xindong Ma, Wen-An Jiang

Publication date: 16 November 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.105959

zbMATH Keywords

fast-slow analysisperiodic bursting behaviorspulse-shaped explosionvan der Pol-Mathieu oscillator

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Singular perturbations for ordinary differential equations (34E15) Nonlinear resonances for nonlinear problems in mechanics (70K30) Nonautonomous smooth dynamical systems (37C60) Relaxation oscillations for ordinary differential equations (34C26)

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Sufficient conditions and criteria for the pulse-shaped explosion related to equilibria in a class of nonlinear systems, Bursting oscillations induced by multiple coexisting attractors in a modified 3D van der Pol-Duffing system, A new route to pulse-shaped explosion of limit cycles and its induced amplitude-modulated bursting, Exploiting multiple-frequency bursting of a shape memory oscillator

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