生物競爭模型中傳遞速度的數值模擬

Numerical Propagation Speed in Diffusive Lotka-Volterra Model

李一耘(Yi-Yun Lee)

指導教授 ： 陳俊全

國立臺灣大學/理學院/應用數學科學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101200

摘要

我們用改良過後的算法做生物競爭模型Lotka-Volterra model 強競爭的數值模擬，使得我們可以保留行波解的資訊與觀察到一般解收斂至行波解的行為，甚至可以定義出一般解的廣義傳遞速度。藉由特定例子中，理論解與數值解的誤差分析，我們可以以可控制的誤差用一般解的漸進行為逼近解不出確切形式的行波解。

關鍵字

生物競爭模型 ； 行波解 ； 反應擴散方程

並列摘要

We use modified numerical scheme to simulate strong competitive diffusive Lotka-Volterra model with 2 species in one dimensional compact domain to preserve the information of traveling wave solutions and the asymptotic behaviours of evolution solutions, and we are able to define generalized propagation speeds of evolution solutions by speed of reference frame. With error analysis in special models, we could approximate unsolvable exact traveling wave solutions by controllable errors.

並列關鍵字

diffusive Lotka-Volterra model ； traveling wave solution ； reaction diffusion system

參考文獻

[1] P. N. Brown. Decay to uniform states in competitive systems. SIAM Journal on Mathematical Analysis, 14(4):659–673, 1983.

[2] P. de Mottoni. Qualitative analysis for some quasilinear parabolic systems. Inst. Math. Pol. Acad. Sci. Zam, 1979.

[3] R. A. Gardner. Existence and stability of travelling wave solutions of competition models: a degree theoretic approach. Journal of Differential equations, 44(3):343–364, 1982.

[4] Y. KanOn. Parameter dependence of propagation speed of travelling waves for competition diffusion equations. SIAM journal on mathematical analysis, 26(2):340–363, 1995.

[5] C. Muratov. A global variational structure and propagation of disturbances in reaction diffusion systems of gradient type. Discrete Continuous Dynamical SystemsB, 4(4):867, 2004.