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Volume 36, Issue 3
Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System

Qiwen Xiu & Dingheng Pi

Ann. Appl. Math., 36 (2020), pp. 282-308.

Published online: 2021-01

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  • Abstract

In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results.

  • Keywords

piecewise smooth systems, limit cycle, sliding cycle, pseudo-homoclinic bifurcation, critical crossing bifurcation $CC$.

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COPYRIGHT: © Global Science Press

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@Article{AAM-36-282, author = {Xiu , Qiwen and Pi , Dingheng}, title = {Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {36}, number = {3}, pages = {282--308}, abstract = {

In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18594.html} }
TY - JOUR T1 - Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System AU - Xiu , Qiwen AU - Pi , Dingheng JO - Annals of Applied Mathematics VL - 3 SP - 282 EP - 308 PY - 2021 DA - 2021/01 SN - 36 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/18594.html KW - piecewise smooth systems, limit cycle, sliding cycle, pseudo-homoclinic bifurcation, critical crossing bifurcation $CC$. AB -

In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results.

Qiwen Xiu & Dingheng Pi. (2021). Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System. Annals of Applied Mathematics. 36 (3). 282-308. doi:
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