The Influence of Nonlinear Cannibalism to Logistic Equation

A single species model with Holling II type cannibalism term is proposed and studied in this paper. Local and global stability property of the system are investigated. By applying the iterative method, we show that the system always admits the unique globally asymptotically stable positive equilibrium. A threshold value R0, which depends on the cannibalism rate and the transform rate, is obtained. Depending on R0 > 1, R0 = 1 or R0 < 1, the final density of the species will smaller or equal to or bigger than the system without cannibalism. Our study shows that if the cannibalism rate is too large, and transform rate is too small, then R0 > 1 and cannibalism has negative effect on the final density of the species, which increase the extinction property of the species.