Existence of traveling wave solutions for diffusive predator–prey type systems

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题名:	Existence of traveling wave solutions for diffusive predator–prey type systems
作者:	Hsu, Cheng-Hsiung;Yang, Chi-Ru;Yang, Ting-Hui;Yang, Tzi-Sheng
贡献者:	淡江大學數學學系
关键词:	Traveling wave;Predator–prey;Wazewski Theorem;LaSalleʼs Invariance Principle;Lyapunov function;Hopf bifurcation theory
日期:	2012-02
上传时间:	2012-01-20 02:48:27 (UTC+8)
出版者:	Maryland Heights: Academic Press
摘要:	In this work we investigate the existence of traveling wave solutions for a class of diffusive predator–prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalleʼs Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
關聯:	Journal of Differential Equations 252(4), pp.3040–3075
DOI:	10.1016/j.jde.2011.11.008
显示于类别:	[應用數學與數據科學學系] 期刊論文

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