Open AccessChaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function
Author(s) -
Hang Zheng,
Yonghui Xia
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021319
Subject(s) - homoclinic orbit , chaotic , piecewise , mathematics , homoclinic bifurcation , manifold (fluid mechanics) , function (biology) , perturbation (astronomy) , piecewise linear function , bifurcation , type (biology) , control theory (sociology) , mathematical analysis , physics , nonlinear system , computer science , mechanical engineering , ecology , control (management) , quantum mechanics , artificial intelligence , evolutionary biology , engineering , biology
In this paper, we study the chaotic behavior of a class of hybrid piecewise-smooth system incorporated into an impulsive effect (HPSS-IE) under a periodic perturbation. More precisely, we assume that the unperturbed system with a homoclinic orbit, it transversally jumps across the first switching manifold by an impulsive stimulation and continuously crosses the second switching manifold. Then the corresponding Melnikov-type function is derived. Based on the new Melnikov-type function, the bifurcation and chaotic threshold of the perturbed HPSS-IE are analyzed. Furthermore, numerical simulations are precisely demonstrated through a concrete example. The results indicate that it is an extension work of previous references.