Understanding of plankton patterns and complex spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton populations

Abstract

In this paper, I have proposed a mathematical model for aquatic ecosystem with three interacting species, toxin-producing phytoplankton (TPP), non-toxin producing phytoplankton (NTP) and zooplankton with Holling type II functional responses. I have carried out a detail study of stability analysis for the non-spatial and spatial model systems and obtained the conditions for diffusive instability. I have also performed the numerical simulation for a particular set of parameter values which is realistic for natural planktonic system. The numerical results revealed the following: (i) dominant TPP population is under control which is essential for aquatic systems, (ii) cyclic behavior of NTP, TPP and zooplankton population in heterogeneous biomass distribution, and (iii) the evolution of patchy non-Turing patterns. The overall result may be useful for sustainability and maintenance of biodiversity of aquatic systems.

Keywords

• toxin-producing phytoplankton
• diffusive instability
• turing domain
• spatio-temporal pattern