Spreading speed and wavefronts for parabolic functional differential equations with spatio-temporal delays

The existence of traveling wavefronts and the spreading speed for a kind of general reaction–diffusion system with spatio-temporal delays are investigated. We obtain the conclusion that there is c∗>0c∗>0 being the asymptotic speed of spread and the minimal speed for the system. Some more delicate analysis techniques have been developed to make the forms of the kernel function g(t,x)g(t,x) and the function ff more flexible in our paper. A pair of super-solution and sub-solution have been constructed in order that the existence of traveling wavefronts can be guaranteed. There is a biological model as an example in this article, which is coincident with this system.