Numerical Study in Reaction-Diffusion-Advection Models with Periodic Heterogeneous Environments

週期異構環境的反應擴散對流模型之數值研究

謝函恩(Han-En Hsieh)

指導教授 ： 王偉成 ； 林文偉

國立清華大學/理學院/數學系/碩士(2010年)

摘要

In this article we study a Lotka-Volterra reaction-di¤usion-advection model arising from the evolution of conditional dispersal of two competing species. In this model two species can choose their own preference of living environ- ment based on di¤erent dispersal strategies. The dispersal behavior may produce coexistence of two species under heterogeneous environment. Our main purpose is to …nd out some coexisting periodic solutions by using dif- ferent numerical methods. We …rst introduce some basic numerical schemes, like forward Euler method, backward Euler method and Runge-Kutta method to solve the reaction-di¤usion-advection system. In addition, we also use Poincare section method to examine the behavior of solutions. Although we have not found any nontrivial coexisting periodic solutions, we have a better understanding for the problem. keywords: Evolution of conditional dispersal, reaction, advection, di¤u- sion, Euler Method, Runge-Kutta Method .

關鍵字

分散的演變 ； 反應 ； 對流 ； 競爭

並列摘要

無資料

並列關鍵字

Evolution of dispersal ； reaction ； advection ； competition

參考文獻

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