In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A bri...The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.展开更多
non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to ...non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.展开更多
This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established...This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.展开更多
In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there...In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.展开更多
基金Partially supported by the National Basic Research Program of China,973 Project (No. 2005CB321902)the Key Lab of Random Complex Structures and Data Science,CAS
文摘In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
基金Project supported by NNSF of China(19971026 10271044) and Scientific Research Fund of Educational Department of Anhui Province.
文摘The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.
基金supported by the Key Lab of Random Complex Structures and Data Science,CAS(Grant No.2008DP173182)the National Basic Research Program of China (973 Project)(Grant No.2005CB321902)
文摘non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.
基金Project supported by NNSF of China (No:19971026).
文摘This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.
基金This research was partially supported by tlie National Natural Science Foundation of China(11871231,11,526095).
文摘In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.
