Travelling Wave Solutions For A Class Of Integral-differential Systems With Delay

In this paper, we study the existence of travelling wave solutions for a delayed Lotka-Volterra integral-differential competition modelwhich is allowed to have more than two equilibria. Specifically, we establish the existence of traveling waves for our model applying the results on the existence of traveling waves for recursions in Li and Zhang[20]. Firstly, we define an important extended real number c+* and build the relation between c+* and the speeds of travelling wave solutions for delay recursions. Secondly, we transfer the competitive system into the cooperative system by changing the variable. And then, by constructing the suitable upper-lower solutions and using the comparison principle, Arzala-Ascoli theory and so on, we verify that the hypothesis of the existence of traveling waves for recursions is held on the cooperative model. So, finally, the result on the existence of traveling waves for recursions allows us infer that the finite positive number c+* can be characterized as the slowest speed of travelling wave solutions connecting two mono-culture equilibria or connecting a mono-culture and the coexistence equilibrium.