ON PERIODIC SOLUTIONS OF LIÉNARD TYPE EQUATIONS-Reference-Cited by-同舟云学术

ON PERIODIC SOLUTIONS OF LIÉNARD TYPE EQUATIONS

Published:2013-12-01 Issue:5 Volume:18 Page:708-716
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
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Author:

Atslega Svetlana¹,Sadyrbaev Felix²

Affiliation:

1. Latvia University of Agriculture 2 Liela Street, LV-3001 Jelgava, Latvia

2. Daugavpils University Parades str. 1, LV-5400 Daugavpils, Latvia

Abstract

The Liénard type equation x'' + f(x, x')x' + g(x) = 0 (i) is considered. We claim that if the associated conservative equation x'' + g(x) = 0 has period annuli then a dissipation f(x, x') exists such that a limit cycle of equation (i) exists in a selected period annulus. Moreover, it is possible to define f(x, x') so that limit cycles appear in all period annuli. Examples are given. A particular example presents two limit cycles of non-convex shape in two disjoint period annuli.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

Reference8 articles.

1. Configurations of limit cycles and planar polynomial vector fields

2. Differential Equations and Dynamical Systems

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