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Limit cycles of polynomial differential systems bifurcating from the periodic orbits of a linear differential system in Rd by Jaume Llibre; Amar Makhlouf is a Mathematics article available to read on EtoBox.

What is Limit cycles of polynomial differential systems bifurcating from the periodic orbits of a linear differential system in Rd about?

Let P k (x 1 , . . . , x d ) and Q k (x 1 , . . . , x d ) be polynomials of degree n k for k = 1, 2, . . . , d. Consider the polynomial differential system in R d defined by Suppose that n k = n 2 for k = 1, 2, . . . , d. Then, by applying the first order averaging method this system has at most (n -1)n d-2 /2 limit cycles bifurcating from the periodic orbits of the same system with ε = 0; and by applying the second order averaging method it has at most (n -1)(2n -1) d-2 limit cycles bifurcating from the periodic orbits of the same system with ε = 0. We provide polynomial differential systems reaching these upper bounds. In fact our results are more general, they provide the number of limit cycles for arbitrary n k .

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Author

Jaume Llibre; Amar Makhlouf

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0007-4497)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)