The global stability and pattern formations of a predator-prey system with consuming resource

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• 作者：Liting Fang ^{litingfangmath@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jinfeng Wang ; ^{jinfengwangmath@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Global stability ; Pattern formation
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：58
• 期：Complete
• 页码：49-55
• 全文大小：549 K

文摘

The paper deals with a model that describes a predator–prey system with a common consuming resource. We use Lyapunov functions to prove the global stability of the kinetic system and the diffusive system. The existence of non-constant positive steady state solutions is shown to identify the range of parameters of spatial pattern formation for the cross-diffusion system.