Convergence to generalized transition waves for some Holling–Tanner prey–predator reaction–diffusion system
Convergence to generalized transition waves for some Holling–Tanner prey–predator reaction–diffusion system
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DOI：
10.1016/j.matpur.2012.10.009
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发表时间：
2013-07
期刊：
影响因子：
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通讯作者：
A. Ducrot
中科院分区：
文献类型：
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作者：
A. Ducrot
这篇手稿致力于研究霍林-坦纳猎物-捕食者反应-扩散系统的一些传播特性。我们更特别关注引入捕食者在最初猎物数量较多的某些环境中的入侵。我们首先证明，对于任意维问题，系统具有传播速度特性。我们为一维系统得出了更精确的信息，研究了该系统的长时间行为，并证明该解（在某种意义上）收敛于具有某些确定的全局平均传播速度的广义过渡波。
This manuscript is devoted to the study of some spreading properties of Holling–Tanner prey–predator reaction–diffusion system. We more particularly focus on the invasion of introduced predator in some environment which is initially well-populated of prey. We first prove that, for the arbitrary dimensional problem, the system has a spreading speed property. We derive more precise information for the one-dimensional system for which the long time behaviour is studied and it is proved that the solution converges (in some sense) towards a generalized transition wave with some determined global mean speed of propagation.