Analyzing wave patterns in a fractional-diffusion-advection predator-prey model

Abstract

In this paper we consider a fractional-diffusion-advection predator-prey model. We analyse traveling wave patterns and show that the model has hetroclinic trajectories connecting two steady state solutions In this paper we consider a fractional-diffusion-advection predator-prey model. We analyse traveling wave patterns and show that the model has hetroclinic trajectories connecting two steady state solutions and corresponding to traveling waves. We also conclude some numerical results in a parameter range. Finally, we numerically find time-dependent solutions and provide simulations in order to support these results concerning traveling wave behavior.