Limit cycles of generalized Liénard polynomial differential systems via averaging theory

Belén García, Jaume Llibre and Jesús S. Pérez del Río

Chaos, Solitons & Fractals, 2014, vol. 62-63, 1-9

Abstract: Using the averaging theory of first and second order we study the maximum number of limit cycles of the polynomial differential systemsẋ=y,ẏ=-x-ε(h1(x)+p1(x)y+q1(x)y2)-ε2(h2(x)+p2(x)y+q2(x)y2),which bifurcate from the periodic orbits of the linear center ẋ=y,ẏ=-x, where ε is a small parameter. If the degrees of the polynomials h1,h2,p1,p2,q1 and q2 are equal to n, then we prove that this maximum number is [n/2] using the averaging theory of first order, where [·] denotes the integer part function; and this maximum number is at most n using the averaging theory of second order.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:62-63:y:2014:i::p:1-9

DOI: 10.1016/j.chaos.2014.02.008

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