Algebraic limit cycles in polynomial systems of differential equations

作者：Llibre, Jaume^*; Zhao, Yulin

来源：Journal of Physics A-Mathematical and Theoretical, 2007, 40(47): 14207-14222.

DOI：10.1088/1751-8113/40/47/012

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.

• 出版日期2007-11-23
• 单位中山大学