Abstract: We considered the spatial dynamic behavior of a predatorprey system with time delay and nonlinear prey harvesting effect. First, we obtained the condition of Hopf bifurcation and Turing bifurcation by using stability theory and bifurcation theory, and then numerical simulations show that the system has rich dynamic behavior. Numerical results show that time delay and diffusion can not only affect the formation of Turing patterns, such as spot, stripe and the coexistence of the two types, but also affect the formation of spiral patterns.

Key words: spiral pattern, predatorprey system, time delay, Hopf bifurcation