INTEGRABILITY AND LINEARIZABILITY FOR A CLASS OF CUBIC KOLMOGOROV SYSTEMS  

作　　者：Qinlong Wang , Haitao Wu (School of Information and Mathematics, Yangtze University, Jingzhou 434023, Hubei) 

出　　处：《Annals of Differential Equations》2010年第4期442-449,共8页微分方程年刊（英文版）

基　　金：supported by the Science Fund of Hubei Education Department(Q20091209)

摘　　要：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.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.

关 键 词：cubic Kolmogorov system INTEGRABILITY LINEARIZABILITY 

分 类 号：O175[理学—数学]