Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting - Wenjing Gao; Yihui Tong; Lihua Zhai; Ruizhi Yang; Leiyu Tang (Advances in Difference Equations, 2019)
Abstract In this paper, we study a predator–prey model with delay and harvesting on predator. We give the conditions for stability and Turing instability of coexisting equilibrium by analyzing the eigenvalue spectrum. By using delay as a bifurcation parameter we give conditions for occurrence of Hopf bifurcation. We investigate the property of bifurcating period solutions by calculating the normal form. We perform some numerical simulations to support our theoretical result. Our results show that diffusion and delay are two factors that should be considered in establishing the predator–prey model, since they can induced the Turing instability and spatially bifurcating period solutions.