強競爭系統之傳播方向

Abstract

我們研究一個定義於一維空間，具有非線性種間競爭項的雙物種 Lotka-Volterra 競爭擴散系統。受到 Girardin 與 Nadin 對經典強競爭系統所建立之「團結非力量」定理的啟發，我們分析當種間競爭率趨近無限大時，行波解的漸近行為。此外，我們明確刻畫了在此模型中傳播方向如何依賴於擴散係數。

We study a two species Lotka-Volterra competition diffusion system with nonlinear interspecific competition terms in one spatial dimension. Motivated by the "unity is not strength" theorem of Girardin and Nadin for classical strongly competitive systems, we analyze the asymptotic behavior of traveling wave profiles as the interspecific competition rate tends to infinity. In addition, we characterize explicitly how the propagation direction depends on the diffusion rates in our model.