Uniqueness of limit cycles for Liénard differential equations of degree four

By Chengzhi Li, Jaume Llibre. 2012

90 citations recorded by the source corpus.

Abstract We prove that any classical Lienard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C.C. Pugh (1977) [4] about the number of limit cycles for polynomial Lienard differential equations for n = 4 .

Subfields: Biochemistry, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/135fc08a6df82f9782c56ca64a99c97d522f4540

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biochemistry

1. Jaume Llibre

In Geometry and Topology

1. Douglas Duarte Novaes
2. Jaume Llibre
3. Marco Antonio Teixeira
4. Maoan Han
5. Xiang Zhang
6. Maite Grau
7. Jaume Giné Mesa
8. C. A. Rodrigues

In Statistical and Nonlinear Physics

1. Douglas Duarte Novaes
2. Jaume Llibre
3. Marco Antonio Teixeira
4. Maoan Han
5. Xiang Zhang
6. C. A. Rodrigues
7. Jaume Giné Mesa
8. Maite Grau

Citations in the corpus

• Higher order averaging theory for finding periodic solutions via Brouwer degree (2014, background): “In a recent work of Giné, Grau and Llibre [12] the averaging theory for computing periodic solutions was developed to an arbitrary order in ε for differential equations of one variable.”