# American Institute of Mathematical Sciences

August  2015, 20(6): 1663-1684. doi: 10.3934/dcdsb.2015.20.1663

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

 1 Department of Mathematics, University of Louisville, Louisville, KY 40292 2 School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281 3 School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States

Received  November 2013 Revised  February 2015 Published  June 2015

We study a cooperative system of integro-differential equations. It is shown that the system in general has multiple spreading speeds, and when the linear determinacy conditions are satisfied all the spreading speeds are the same and equal to the spreading speed of the linearized system. The existence of traveling wave solutions is established via integral systems. It is shown that when the linear determinacy conditions are satisfied, if the unique spreading speed is not zero then it may be characterized as the slowest speed of a class of traveling wave solutions. Some examples are presented to illustrate the theoretical results.
Citation: Changbing Hu, Yang Kuang, Bingtuan Li, Hao Liu. Spreading speeds and traveling wave solutions in cooperative integral-differential systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1663-1684. doi: 10.3934/dcdsb.2015.20.1663
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