On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings DOI
Chun Zhang,

Qiaoxia Tang

Physica Scripta, Journal Year: 2023, Volume and Issue: 99(1), P. 015204 - 015204

Published: Dec. 6, 2023

Abstract Multiple timescale effects can be reflected bursting oscillations in many classical nonlinear oscillators. In this work, we are concerned about the induced by two damped Helmholtz-Rayleigh-Duffing oscillator (written as DHRDO for short) excited slow-changing parametrical and external forcings. By using trigonometric function variation authenticating slow excitations a slowly varying state variable, time-varying rewritten new time-invariant system. Then, critical conditions of some typical bifurcations presented bifurcation theory. With help analyses, six patterns, i.e., ‘Hopf/Hopf-Hopf/Hopf’ bursting, ‘fold/Homoclinic-Hopf/Hopf’ ‘fold/Homoclinic/Hopf’ ‘Hopf/fold/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’ explored slow/fast decomposition method other techniques. Our findings provide different forms oscillation modes well patterns. addition, use numerical simulation to prove correctness theoretical analyses.

Language: Английский

Occurrence of mixed-mode oscillations in a system consisting of a Van der Pol system and a Duffing oscillator with two potential wells DOI
Weipeng Lyu, Shaolong Li, Juanjuan Huang

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: 112(8), P. 5997 - 6013

Published: Feb. 27, 2024

Language: Английский

Citations

2
On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings DOI
Chun Zhang,

Qiaoxia Tang

Physica Scripta, Journal Year: 2023, Volume and Issue: 99(1), P. 015204 - 015204

Published: Dec. 6, 2023

Abstract Multiple timescale effects can be reflected bursting oscillations in many classical nonlinear oscillators. In this work, we are concerned about the induced by two damped Helmholtz-Rayleigh-Duffing oscillator (written as DHRDO for short) excited slow-changing parametrical and external forcings. By using trigonometric function variation authenticating slow excitations a slowly varying state variable, time-varying rewritten new time-invariant system. Then, critical conditions of some typical bifurcations presented bifurcation theory. With help analyses, six patterns, i.e., ‘Hopf/Hopf-Hopf/Hopf’ bursting, ‘fold/Homoclinic-Hopf/Hopf’ ‘fold/Homoclinic/Hopf’ ‘Hopf/fold/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’ explored slow/fast decomposition method other techniques. Our findings provide different forms oscillation modes well patterns. addition, use numerical simulation to prove correctness theoretical analyses.

Language: Английский

Citations

0