| Summary: | 碩士 === 國立中正大學 === 數學系應用數學研究所 === 106 === In this thesis, we will discuss the stochastic behavior of a predator-prey model and discuss the wave speed as the parameter varied on the diffusivity in the predator-prey model.
First chapter, we follow Petrovskll and Malchow (A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions, Mathematical and Computer Modelling, 29 (1999) , pp. 49-63) to sketch deterministic case and simulate the numerical result for ve different states in chapter 1. Then, we follow Gillespie (A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions, Journal of Computation Physics, 22 (1976), pp. 403-434) and Karig (Introduction to Stochastic Simulation with the Gillespie Method, available at https://www.cs.princeton.edu/picasso/seminarsS05/Karig slides.pdf, April 18, 2005, pp. 1-36) and Gillespie (The chemical Langevin equation, Journal of Chemical Physics, 113 (2000), pp. 297-306) to sketch the Gillespie method and Langevin method in chapter 1.
Second chapter, we follow Doedel (Lecture Notes on Numerical Analysis of Nonlinear Equations; available at http://users.encs.concordia.ca/ doedel/) and Shui-Han (Computational study of waves in predator-prey system, Department of Applied Mathematics National Chung Cheng University, (2015), pp. 5-11) to sketch the continuation method in chapter 2.
Appendix, we will follow Martin Griffiths (The golden ratio and equilateral triangles, Mathematics Magazine Note. 99.22, (2015), pp.342-346) to sketch the relationship between sides and corner angle in two different size of equilateral n-polygons.
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