TY - JOUR

T1 - Algebraic limit cycles in polynomial systems of differential equations

AU - Llibre, Jaume

AU - Zhao, Yulin

PY - 2007/11/23

Y1 - 2007/11/23

N2 - Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4. © 2007 IOP Publishing Ltd.

AB - Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4. © 2007 IOP Publishing Ltd.

U2 - https://doi.org/10.1088/1751-8113/40/47/012

DO - https://doi.org/10.1088/1751-8113/40/47/012

M3 - Article

VL - 40

SP - 14207

EP - 14222

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -