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
The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the syst...The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using computer algebra system such as Mathematica or Maple, and some good methods are given to obtain the sufficient conditions.展开更多
This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.
In this paper we use the theory of symmetric covariant tensor space and simultaneous classification method to successively classify the so-called cubic Kolmogorov type system. As an application of the result obtained,...In this paper we use the theory of symmetric covariant tensor space and simultaneous classification method to successively classify the so-called cubic Kolmogorov type system. As an application of the result obtained, we characterize the local phase portrait of the isolated critical points at infinity for a class of that system, and give some necessary and sufficient conditions for all its trajectories to be bounded.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.
基金supported by the Science Fund of Hubei Education Department(Q20091209)
文摘The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using computer algebra system such as Mathematica or Maple, and some good methods are given to obtain the sufficient conditions.
文摘This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles.
文摘In this paper we use the theory of symmetric covariant tensor space and simultaneous classification method to successively classify the so-called cubic Kolmogorov type system. As an application of the result obtained, we characterize the local phase portrait of the isolated critical points at infinity for a class of that system, and give some necessary and sufficient conditions for all its trajectories to be bounded.
