有兩部分如下。1.我們打算研究非齊時馬氏鏈。狀態空間是有限的情形已有結果。狀態空間是可數時，似乎沒有研究。我們打算由Kolmogorov方程切入。首先要瞭解方程是否有解。目標是系統的極限行為。2. 人口模型中的非局部行為。predator–prey 系統裡合作獵捕問題在獵物用Beverton-Holt型式成長時已有工作發表。我們今年的計畫進一步研究Ricker成長型式的合作獵捕問題。我們現在申請的計畫是研究合作獵捕問題中的非局部行為。同樣也可考慮Leslie-Gower 競爭模型中的非局部行為。 ;There are two parts in the proposal.1. Time-inhomogeneous denumerable Markov chains. We plan to investigate time-inhomogeneous denumerable Markov chains. When the state space is finite, the asymptotic behavior of the process is well understood by analysing the Kolmogorov forward equations associated with the system. When the state space is countable, we should be able to adopt the same technique to show the existence of solutions and then its asymptotic behavior under some conditions. A crucial step is to get some tightness results so the mass will not spread too far. 2. Global dynamics of population models. We will continue our study on cooperative hunting in a discrete predator–prey system. The goal is to study whether system is persistent and whether every positive solution converges. Same issue exists for Leslie-Gower competition models, for which we had obtained global results for some special systems.
