在週期異質性環境下之反應擴散平流模型的生態問題研究
Abstract
本計畫將研究兩個相互競爭的物種之Lotka-Volterra反應擴散平流模型，在改變食物資源分佈下，觀察其物種數量演變的情形。將在二維有界的定義域下，給予週期的異質性環境，進行數值模擬與分析。本計畫將分為三個部分執行：（1）計算方法的建立-在一維定義域下，設定週期的異質性環境，找出有效率且準確的的離散方法來求得競爭模型的解；（2）時間相關的主題研究-針對二維定義域問題，在不同的週期異質性環境設定與參數下進行模擬，期望找尋出不同的物種競爭演變結果；（3）與時間無關的主題研究-剖析分歧現象是否存在於此模型上，進而刻畫出分歧類型，以及進行二維問題上物種競爭結果的穩定性分析。
In this project, to study evolution of conditional dispersal, a Lotka-Volterra reaction-diffusion-advection model for two competing species in a periodic heterogeneous environment is proposed and investigated. The two species are assumed to be identical except for their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but with slightly different random dispersal or advection rates. We hope to develop a high efficient numerical algorithm with suitable discretization methods to deal with this reaction-diffusion-advection model for solving periodic solutions. Moreover, we would like to examine the stability of these solutions and bifurcation phenomena.
In this project, to study evolution of conditional dispersal, a Lotka-Volterra reaction-diffusion-advection model for two competing species in a periodic heterogeneous environment is proposed and investigated. The two species are assumed to be identical except for their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but with slightly different random dispersal or advection rates. We hope to develop a high efficient numerical algorithm with suitable discretization methods to deal with this reaction-diffusion-advection model for solving periodic solutions. Moreover, we would like to examine the stability of these solutions and bifurcation phenomena.