A universal constant for semistable limit cycles

Autor(es)

Artes, Joan C. ^[1] ; Llibre, Jaume ^[2] ; Teixeira, Marco Antonio ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona. Dept Matemat

^[2] Univ Autonoma Barcelona. Dept Matemat

^[3] Univ Estadual Campinas. Dept Matemat

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL & APPLIED MATHEMATICS; v. 30, n. 2, p. 463-483, 2011.
• Citações Web of Science: 0

Resumo

We consider one-parameter families of 2-dimensional vector fields X-mu having in a convenient region R a semistable limit cycle of multiplicity 2m when mu = 0, no limit cycles if mu (sic) 0, and two limit cycles one stable and the other unstable if mu (sic) 0. We show, analytically for some particular families and numerically for others, that associated to the semistable limit cycle and for positive integers n sufficiently large there is a power law in the parameter mu of the form mu(n) approximate to Cn(alpha) < 0 with C, alpha is an element of R, such that the orbit of X-mu n through a point of p is an element of R reaches the position of the semistable limit cycle of X-0 after given n turns. The exponent alpha of this power law depends only on the multiplicity of the semistable limit cycle, and is independent of the initial point p is an element of R and of the family X-mu. In fact alpha = -2m/(2m - 1). Moreover the constant C is independent of the initial point p is an element of R, but it depends on the family X-mu and on the multiplicity 2m of the limit cycle Gamma. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático