Rational limit cycles on Bernoulli and Riccati equations

JOURNAL OF GEOMETRY AND PHYSICS

卷:155

Article

Valls, Claudia¹ 

[1] Univ Lisbon, Inst Super Tecn, Dept Matemat, Ave Rovisco Pais1049-001, Lisbon, Portugal

关键词: Algebraic limit cycles;    Rational limit cycles;    Bernoulli equations;   

DOI  :  10.1016/j.geomphys.2020.103705

来源: Elsevier

【 摘 要 】

In this paper we deal with Bernoulli equations dy/dx = A(x)y(n) + B(x)y, where A(x) and B(x) are real polynomials with A(x) not equivalent to 0 and n >= 3. We prove that these Bernoulli equations can have at most 2 rational limit cycles if n is odd and at most one rational limit cycle if n is even. We also provide examples of Bernoulli equations with these numbers of rational limit cycles. Moreover we deal with the Riccati equations dy/dx = A(0)(x) + A(1)(x)y + A(2)(x)y(2), where A(0)(x), A(1)(x), A(2)(x) are real polynomials with A(2)(x) not equivalent to 0. We prove that these Riccati equations can have at most 2 rational limit cycles. We also provide examples of Riccati equations with these numbers of rational limit cycles. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free