Almost periodic solution of a non-autonomous model of phytoplankton allelopathy

Abstract

In this paper, a non-autonomous two species competitive allelopathic phytoplankton model in presence of a discrete time delay is considered. We have obtained the sufficient conditions for permanence along with existence-uniqueness of an almost periodic solution. Sufficient conditions are derived for the existence of unique almost periodic solution. Analytical findings are supported through exhaustive numerical simulations. With the help of the numerical example, we have demonstrated that initial density dependent almost periodic co-existence is possible in some situations when parameter values fail to satisfy all the conditions of permanence.