A solution to the evolution-related Truscott-Brindley model for the generalized phytoplankton-zooplankton populations

TL;DR

This paper extends the Truscott-Brindley model to include spatially structured phytoplankton and zooplankton populations, using Boubaker polynomials expansion and stability analysis to better understand their dynamics.

Contribution

It introduces a generalized model incorporating spatial structure and applies BPES for solution, advancing the understanding of phytoplankton-zooplankton interactions.

Findings

Model demonstrates stable population dynamics under certain conditions

Boubaker polynomials expansion effectively solves the model equations

Stability analysis identifies parameters for sustainable populations

Abstract

Phytoplankton are tiny floating plants (algae) living in oceans. In the process of photosynthesis, phytoplankton produces half of the world's oxygen. Moreover, by primary production, death and sinking, they transport carbon from the ocean's surface layer to marine sediments. There are many species of phytoplankton that can be distinguished according to morphology. In this paper, we investigate the generalised Truscott-Brindley model of the dynamics of zoologically defined interacting populations which have spatial structure. Specifically, we consider conjointly marine phytoplankton and zooplankton populations, and model them as an excitable medium. The resolution using the Boubaker polynomials expansion scheme (BPES) along with stability analysis is carried out.