This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system ma...This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.展开更多
In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degreesof invari...In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degreesof invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that anyholomorphic foliation of degree 2 does not have cubic limit cycles.展开更多
基金The NSF of Liaoning provinceFoundation of returned doctors and Foundation of LiaoningEducation Committee.
文摘This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.
文摘In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 19901013).
文摘In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degreesof invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that anyholomorphic foliation of degree 2 does not have cubic limit cycles.
