Stability of The Reaction-Diffusion Predator Prey Model

Stability of The Reaction-Diffusion Predator Prey Model

林正晅(Lin Cheng-Hsuan)

指導教授 ： 張幼賢

國立臺灣師範大學/理學院/數學系/碩士(2017年)

https://doi.org/10.6345/NTNU202203027

摘要

本論文探討一個包含了Reaction-diffusion 的predator-prey model，此模型出自Lakshmi Narayan Guin 的Spatial patterns through Turing instability
in a reaction–diffusion 這篇論文。
在第二章裡介紹了本篇論文所使用的方法Liapunov-liked method，這方法主要是做一個Dichotomy 的動作，藉由第三章計算出模型中線性部分的eigenvalues 後以此方法去探討模型解的穩定情形。

關鍵字

掠食者—獵物方程 ； 反應擴散 ； 二分法

並列摘要

In this paper we consider reaction-diffusion system of predator prey model. We use the Liapunov-liked method to discuss the asymptotic behavior of the solutions
and the stabilities of three equilibrium points.

並列關鍵字

predator-prey ； Reaction diffusion, ； Dichotomy

參考文獻

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[2] Lakshmi Narayan Guin, Spatial patterns through Turing instability in a reaction-diffusion predator-prey model, Mathematics and Computers in Simulation, Volume 109, Issue C, March 2015, 174-185.

[3] J.D.Murray, Discussion: Turing's theory of morphogensis-its influence on modeling biological pattern and form, Bull. Math. Biol. 52(1990) 119-152.

[4] Y. H. Chang, R. H. Martin, Dichotomies for Abstract Semilinear Equations, Journal of Mathematical Analysis and Applications 189, no.1, 1995, 194-214.

[5] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.