On the limit cycles of the floquet differential equation

Jaume Llibre; Ana Rodrigues

doi:https://doi.org/10.3934/dcdsb.2014.19.1129

On the limit cycles of the floquet differential equation

Jaume Llibre, Ana Rodrigues

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x(t) = Ax(t) + ε(B(t)x(t) + b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n × n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory but only uses linear algebra.

Original language	English
Pages (from-to)	1129-1136
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	19
Issue number	4
DOIs	https://doi.org/10.3934/dcdsb.2014.19.1129
Publication status	Published - 1 Jan 2014

Keywords

Averaging theory
Floquet differential equation
Limit cycle
Periodic solution

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T1 - On the limit cycles of the floquet differential equation

AU - Llibre, Jaume

AU - Rodrigues, Ana

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N2 - We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x(t) = Ax(t) + ε(B(t)x(t) + b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n × n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory but only uses linear algebra.

AB - We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x(t) = Ax(t) + ε(B(t)x(t) + b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n × n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory but only uses linear algebra.

KW - Averaging theory

KW - Floquet differential equation

KW - Limit cycle

KW - Periodic solution

UR - https://ddd.uab.cat/record/150741

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DO - https://doi.org/10.3934/dcdsb.2014.19.1129

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EP - 1136

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 4

ER -