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...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.展开更多
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)
文摘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.
