Traveling wave solutions in a diffusive predator-prey system with Holling type-III functional response

This work concerns with the existence of traveling wave solutions for the following diffusive predator-prey type system with Holling type-III functional response: u t(x, t) = d(1) u (xx) (x, t) + Au(x, t) (1 - u(x,t/K)-phi (u(x, t))w(x, t), w(t) (x, t) = d(2) w(xx)(x, t) + w(x, t) (mu phi(u(x, t)) - C). where all parameters are positive which will be mentioned later. The traveling wave solutions are established in R-4, which is a heteroclinic orbit connecting the boundary equilibrium and the positive equilibrium. Applying the methods of Wazewski Theorem and LaSalle's Invariance Principle, and constructing a Liapunov function, we obtain the existence of traveling wave solutions. We also discuss some possible biological implications of the existence of these waves.