Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation-Reference-Cited by-同舟云学术

Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation

Published:2023-08-28 Issue:11 Volume:78 Page:1015-1030
ISSN:0932-0784
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Hu Sengen¹,Zhou Liangqiang¹^ORCID

Affiliation:

1. School of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , 210016 , China

Abstract

Abstract Chaotic dynamics of a fifth-order extended Duffing-van der Pol system with a non-smooth periodic perturbation and parametric excitation are investigated both analytically and numerically in this paper. With the Fourier series, the system is expanded to the equivalent smooth system. The Melnikov perturbation method is used to derive the horseshoe chaos condition in the cases of homoclinic and heteroclinic intersections. The chaotic features for different system parameters are investigated in detail. The monotonic variation of the coefficients of parametric excitation and non-smooth periodic disturbance is found. With numerical methods, we validate the analytical results obtained by Melnikov’s method. The impact of initial conditions is carefully analyzed by basins of attraction and the effect of non-smooth periodic disturbance on the basin of attraction is also investigated. Besides, the effect of different parameters on the bifurcation pathway into chaotic attractors is examined.

Funder

National Natural Science Foundation of China

China Postdoctoral Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-2023-0117/pdf

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