Patterned Solutions of a Homogenous Diffusive Predator-Prey System of Holling Type-Ⅲ 被引量：1

Patterned Solutions of a Homogenous Diffusive Predator-Prey System of Holling Type-Ⅲ

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摘要 In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis. In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis.

作者 A-ying WAN Zhi-qiang SONG Li-fei ZHENG

机构地区 School of Mathematics and Statistics School of Mining Technology Department of Applied Mathematics

出处《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第4期1073-1086,共14页 应用数学学报（英文版）

基金 Supported by the National Natural Science Foundation of China(No.11461024) Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(No.NJZZ14310) National Higher-education Institution General Research and Development Project(No.2014YB023)

关键词 diffusive predator-prey system Hholling type functional response Hopf bifurcation turing insta-bility. diffusive predator-prey system Hholling type functional response Hopf bifurcation turing insta-bility.

分类号 O175 [理学—基础数学]

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