TY - JOUR
T1 - Limit cycles bifurcating from a perturbed quartic center
AU - Coll, Bartomeu
AU - Llibre, Jaume
AU - Prohens, Rafel
PY - 2011/5/1
Y1 - 2011/5/1
N2 - We consider the quartic center ẋ=-yf(x,y),ẏ=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc ≠ 0. Here we study the maximum number σ of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 ≤ σ ≤ 5[(n - 1)/2] + 14, where [η] denotes the integer part function of η. © 2011 Elsevier Ltd. All rights reserved.
AB - We consider the quartic center ẋ=-yf(x,y),ẏ=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc ≠ 0. Here we study the maximum number σ of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 ≤ σ ≤ 5[(n - 1)/2] + 14, where [η] denotes the integer part function of η. © 2011 Elsevier Ltd. All rights reserved.
U2 - 10.1016/j.chaos.2011.02.009
DO - 10.1016/j.chaos.2011.02.009
M3 - Article
SN - 0960-0779
VL - 44
SP - 317
EP - 334
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 4-5
ER -