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Volume 5, Issue 4
Hopf Cyclicity of a Class of Liénard-Type Systems

Hongwei Shi & Changjian Liu

DOI: 10.12150/jnma.2023.682

J. Nonl. Mod. Anal., 5 (2023), pp. 682-694.

Published online: 2023-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Liénard systems are studied. For two Liénard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results.

  • Keywords

Hopf cyclicity, polynomial and rational polynomial Liénard systems, smooth and piecewise smooth systems.

  • AMS Subject Headings

34C07, 34D10, 37G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-682, author = {Shi , Hongwei and Liu , Changjian}, title = {Hopf Cyclicity of a Class of Liénard-Type Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {682--694}, abstract = {

The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Liénard systems are studied. For two Liénard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.682}, url = {http://global-sci.org/intro/article_detail/jnma/22201.html} }
TY - JOUR T1 - Hopf Cyclicity of a Class of Liénard-Type Systems AU - Shi , Hongwei AU - Liu , Changjian JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 682 EP - 694 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.682 UR - https://global-sci.org/intro/article_detail/jnma/22201.html KW - Hopf cyclicity, polynomial and rational polynomial Liénard systems, smooth and piecewise smooth systems. AB -

The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Liénard systems are studied. For two Liénard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results.

Hongwei Shi & Changjian Liu. (2023). Hopf Cyclicity of a Class of Liénard-Type Systems. Journal of Nonlinear Modeling and Analysis. 5 (4). 682-694. doi:10.12150/jnma.2023.682
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