TY - JOUR

T1 - Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2009/3/15

Y1 - 2009/3/15

N2 - In this paper we classify the centers, the cyclicity of its Hopf bifurcation and their isochronicity for the polynomial differential systems in R2 of arbitrary degree d ≥ 3 odd that in complex notation z = x + i y can be written asover(z, ̇) = (λ + i) z + (z over(z, -))frac(d - 3, 2) (A z3 + B z2 over(z, -) + C z over(z, -)2 + D over(z, -)3), where λ ∈ R and A, B, C, D ∈ C. If d = 3 we obtain the well-known class of all polynomial differential systems of the form a linear system with cubic homogeneous nonlinearities. © 2008 Elsevier Inc. All rights reserved.

AB - In this paper we classify the centers, the cyclicity of its Hopf bifurcation and their isochronicity for the polynomial differential systems in R2 of arbitrary degree d ≥ 3 odd that in complex notation z = x + i y can be written asover(z, ̇) = (λ + i) z + (z over(z, -))frac(d - 3, 2) (A z3 + B z2 over(z, -) + C z over(z, -)2 + D over(z, -)3), where λ ∈ R and A, B, C, D ∈ C. If d = 3 we obtain the well-known class of all polynomial differential systems of the form a linear system with cubic homogeneous nonlinearities. © 2008 Elsevier Inc. All rights reserved.

U2 - https://doi.org/10.1016/j.jde.2008.12.006

DO - https://doi.org/10.1016/j.jde.2008.12.006

M3 - Article

SN - 0022-0396

VL - 246

SP - 2192

EP - 2204

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -