Spreading speeds and traveling wave solutions in cooperative integral-differential systems

We study a cooperative system of integro-differential equations.It is shown that the system in general has multiple spreadingspeeds, and when the linear determinacy conditions are satisfiedall the spreading speeds are the same and equal to the spreadingspeed of the linearized system. The existence of traveling wavesolutions is established via integral systems. It is shown thatwhen the linear determinacy conditions are satisfied, if theunique spreading speed is not zero then it may be characterized asthe slowest speed of a class of traveling wave solutions. Someexamples are presented to illustrate the theoretical results.