Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Jaume Llibre; Bruno D. Lopes; Jaime R. De Moraes

doi:https://doi.org/10.1007/s12346-014-0109-9

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Jaume Llibre, Bruno D. Lopes, Jaime R. De Moraes

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

Abstract

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (Formula presented.) when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. © 2014 Springer Basel.

Original language	English
Pages (from-to)	129-148
Journal	Qualitative Theory of Dynamical Systems
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s12346-014-0109-9
Publication status	Published - 1 Jan 2014

Keywords

Averaging method
Isochronous center
Limit cycle
Periodic orbit
Polynomial vector field

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abstract = "We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (Formula presented.) when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. {\textcopyright} 2014 Springer Basel.",

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N2 - We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (Formula presented.) when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. © 2014 Springer Basel.

AB - We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (Formula presented.) when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. © 2014 Springer Basel.

KW - Averaging method

KW - Isochronous center

KW - Limit cycle

KW - Periodic orbit

KW - Polynomial vector field

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DO - https://doi.org/10.1007/s12346-014-0109-9

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EP - 148

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

SN - 1575-5460

IS - 1

ER -

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Abstract

Keywords

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