A Distributed Delay Model of One Ammensal on two Mutualistic Species

Abstract

In this paper we study the dynamics of one ammensal and two species helping mutually one another. Here the first species(x) ammensal on the other two species (y, z), which are mutually helping one another. A distributed type delay is incorporated in the interaction of second and third species with the first species. Co-existing state of the system is identified and the stability is studied at this point. And numerical simulation is carried out to study the stability of the system using exponential type of kernel. We observed that the delay parameters improved the mutualistic species’ densities.