Pattern formation in a reaction–diffusion rumor propagation system with Allee effect and time delay

This paper analyzes the diffusion behavior of suspicious and infected cabins in cyberspace by establishing a rumor propagation reaction–diffusion model with Allee effect time delay. The Turing instability conditions system are emphatically studied. After considering delay on system, we have studied correlation between stability under influence small homogeneous near equilibrium point; critical condition delay-induced spatial is given as well. Then, prove existence Hopf bifurcation induced some cases. Further possibility coefficient changing time, parameter curves approximate systems means Floquet theory, necessary periodic In numerical simulations, find that variation will change pattern type, periodical affect arrangement crowd gathering area pattern.