One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred...One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.展开更多
We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positi...We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.展开更多
In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and t...In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally,the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.展开更多
As shown in the results of the survey of the confidence of 100 Chinese economists,conducted by China’s Economic Monitoring and Analysis Centre,National Bureau of Statistics,the confidence index of the economists in t...As shown in the results of the survey of the confidence of 100 Chinese economists,conducted by China’s Economic Monitoring and Analysis Centre,National Bureau of Statistics,the confidence index of the economists in the second quarter of 2009 was 5.60,the range of possible indices being from 1 to 9.It was 1.63 points higher than that of the first quarter,continuing the stabilized situation with a trend of rising again.The situation had appeared since the beginning of 2009.展开更多
基金This work is supported by National Science Foundation of China and the Fundes of Institute of Math (opened) Academic Sinica.
文摘One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
文摘We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.
基金Supported by the Natural Science Foundation of China(11401356)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2015JM1008)the Foundation of Weinan Teachers University(No.13YKF004)
文摘In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally,the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.
文摘As shown in the results of the survey of the confidence of 100 Chinese economists,conducted by China’s Economic Monitoring and Analysis Centre,National Bureau of Statistics,the confidence index of the economists in the second quarter of 2009 was 5.60,the range of possible indices being from 1 to 9.It was 1.63 points higher than that of the first quarter,continuing the stabilized situation with a trend of rising again.The situation had appeared since the beginning of 2009.
