Stability and bifurcation analysis of a tri-trophic food chain model with intraguild predation  

作　　者：Evgeniya Giricheva 

机构地区：[1]Institute of Automation and Control Processes Far Eastern Branch of the Russian Academy of Science 5Radio street Vladivostok,690014,Russia

出　　处：《International Journal of Biomathematics》2023年第2期59-84,共26页生物数学学报（英文版）

摘　　要：The dynamics of a three-component model for food web with intraguild predation isconsidered. The model is based on the collection of ordinary differential equations thatdescribe the interactions among prey, intermediate predator and top predator. First,the model without self-limitation of the predators is studied. Boundedness of the systemand existence of non-negative solutions are established. The local stability analysisof the equilibria is carried out to examine the behavior of the system. The possibilityof Hopf bifurcation around non-negative equilibria with consumption rates as bifurcationparameters is studied. Center manifold theorem and the normal form theory areapplied to obtain the formulas for determining the direction of Hopf bifurcation and thestability of bifurcating periodic solutions. Numerical simulations support the analyticalfindings, which show that the extinction of one of the predators can occur under certainrestrictions on the predation rate of the top predator. Subsequently, numerical analysisof the model with self-limitation of the predators is carried out. Simulations reveal thatthe system with intraspecific competition in the predator populations can reproducecoexistence between the three species in resource-rich environment.

关 键 词：Prey-predator model intraguild predation STABILITY Hopf bifurcation 

分 类 号：O17[理学—数学]