Dynamic analysis of a predator cannibalism model with Holling type Ⅱ functional response
In order to study the effect of cannibalism on the predator-prey system,a predator-prey model with cannibalism in predators and Holling type Ⅱ functional response was established.The non-negativity and boundedness of the solutions of the model was proved and sufficient conditions for the existence of the equilibria were given.By the linearization method and the construction of Dulac func-tion,the local and global stability of the equilibria were analyzed.The results show that when the half saturation coefficient of the prey is greater than or equal to the environmental capacity,the model has one unique positive equilibrium which is globally asymptotically stable,otherwise,the model may have multiple positive equilibria.Numerical simulations show that cannibalism is a lifeboat mecha-nism,which makes the predator population survive without the prey.
cannibalismHolling type Ⅱ functional responseglobal stabilityperiodic solution
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