Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

Mauricio Firmino Silva Lima; Jaume Llibre

doi:https://doi.org/10.1016/j.amc.2011.04.069

Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

Mauricio Firmino Silva Lima, Jaume Llibre

Department of Mathematics

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

4 Citations (Scopus)

Abstract

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	9985-9996
Journal	Applied Mathematics and Computation
Volume	217
Issue number	24
DOIs	https://doi.org/10.1016/j.amc.2011.04.069
Publication status	Published - 15 Aug 2011

Keywords

Continuous piecewise linear vector fields
Discontinuous piecewise linear vector fields
Equilibrium point
Invariant cylinder
Limit cycle
Periodic orbit

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title = "Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n",

abstract = "The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed. {\textcopyright} 2011 Elsevier Inc. All rights reserved.",

keywords = "Continuous piecewise linear vector fields, Discontinuous piecewise linear vector fields, Equilibrium point, Invariant cylinder, Limit cycle, Periodic orbit",

author = "Lima, {Mauricio Firmino Silva} and Jaume Llibre",

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AU - Lima, Mauricio Firmino Silva

AU - Llibre, Jaume

PY - 2011/8/15

Y1 - 2011/8/15

N2 - The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Inc. All rights reserved.

AB - The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Inc. All rights reserved.

KW - Continuous piecewise linear vector fields

KW - Discontinuous piecewise linear vector fields

KW - Equilibrium point

KW - Invariant cylinder

KW - Limit cycle

KW - Periodic orbit

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DO - https://doi.org/10.1016/j.amc.2011.04.069

M3 - Article

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EP - 9996

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ER -