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.
The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attructivity and extinction in the system. Applications of our main results to logist...The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attructivity and extinction in the system. Applications of our main results to logistic equation and generalized logistic equation are given. It is shown that our average conditions are improvement of those in Vance and Coddington [J. Math. Biol. 27 （1989） 491-506] and some published literature on the system.展开更多
This work is concerned with controlled stochastic Kolmogorov systems.Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise th...This work is concerned with controlled stochastic Kolmogorov systems.Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control,this paper is devoted to designing numerical methods for approximation.Different from the existing literature on numerical methods for stochastic controls,the Kolmogorov systems take values in the first quadrant.That is,each component of the state is nonnegative.The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent)the controlled diffusion.The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works.Convergence of the numerical scheme is proved under suitable conditions.展开更多
Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmo...Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous Markovian processes with discrete states and continuous time, are listed in symmetric matrix form. Properties of symmetry of matrix of subsystem failure and recovery flow intensity are analyzed. Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained. It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order. Depending upon intensity of failure and recovery flows, four roots of characteristic equation are analytically found out. Analytical formulae for state probability of interactive technical system depending upon the roots of characteristic equation are determined using structurally ordered symmetric determinants, involving proper column of set initial data as well as subsystem failure and recovery flow intensity are proposed.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The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attructivity and extinction in the system. Applications of our main results to logistic equation and generalized logistic equation are given. It is shown that our average conditions are improvement of those in Vance and Coddington [J. Math. Biol. 27 （1989） 491-506] and some published literature on the system.
基金ARO W911NF1810334NSF under EPCN 1935389the National Renewable Energy Laboratory(NREL)。
文摘This work is concerned with controlled stochastic Kolmogorov systems.Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control,this paper is devoted to designing numerical methods for approximation.Different from the existing literature on numerical methods for stochastic controls,the Kolmogorov systems take values in the first quadrant.That is,each component of the state is nonnegative.The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent)the controlled diffusion.The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works.Convergence of the numerical scheme is proved under suitable conditions.
文摘Technical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous Markovian processes with discrete states and continuous time, are listed in symmetric matrix form. Properties of symmetry of matrix of subsystem failure and recovery flow intensity are analyzed. Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained. It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order. Depending upon intensity of failure and recovery flows, four roots of characteristic equation are analytically found out. Analytical formulae for state probability of interactive technical system depending upon the roots of characteristic equation are determined using structurally ordered symmetric determinants, involving proper column of set initial data as well as subsystem failure and recovery flow intensity are proposed.
