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
It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynami...It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.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.
文摘It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.
