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標題: 利用Liapunov-Schmidt化簡法與數值延續法來探討捕食者-被捕者的數學模式
Liapunov-Schmidt Reduction and Numerical Continuation for Predator-Prey Models
作者: 蕭竣中
Hsiao, Chun-Chung
關鍵字: Predator-prey models;捕食者-被捕者的數學模型;Liapunov-Schmidt reduction;bifurcation;numerical continuation;two-gird method;Liapunov-Schmidt化簡法;分支,延續法;雙重網格法
出版社: 應用數學系所
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We study bifurcation scenario of three predator-prey models. The Liapunov-Schmidt reduction is applied to compute normal forms of these models. We show that the bifurcations are all transcritical. We also study a two-grid centered difference discretization scheme with two-loop continuation algorithms for tracing solution curves of reaction-diffusion systems. Both linear and quadratic approximations of the operator equations are exploited to derive the scheme. A numerical continuation algorithm is exploited to trace solution curves of the models. The theoretical proofs are verified by our numerical results.
其他識別: U0005-1707200612452300
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