Existence and asymptotic of traveling wave fronts for the delayed Volterra-type cooperative system with spatial diffusion
Existence and asymptotic of traveling wave fronts for the delayed Volterra-type cooperative system with spatial diffusion
In the paper, we are concerned with the existence and the exponential asymptotic behavior of traveling waves for the delayed Volterra-type cooperative system with nonquasimonotone condition $$\begin{aligned} \textstyle\begin{cases} \frac{\partial{u_{1}}(x,t)}{\partial t}={D_{1}}\frac{\partial ^{2}{u_{1}}(x,t)}{\partial x^{2}} + r_{1}u_{1}(x,t)[ 1 - a_{1}u_{1}(x,t) - b_{1}u_{1}(x,t-\tau_{1}) + c_{1}u_{2}(x,t-\tau_{2})],\\ \frac{\partial{u_{2}}(x,t)}{\partial t}={D_{2}}\frac{\partial ^{2}{u_{2}}(x,t)}{\partial x^{2}} + {r_{2}}{u_{2}}(x,t)[1 - {a_{2}u_{2}}(x,t) - …