Eur. Phys. J. Plus (2022) 137: 368
https://doi.org/10.1140/epjp/s13360-022-02566-1

Regular Article

Effect of seasonality on a nutrient–plankton system with toxicity in the presence of refuge and additional food

¹ Department of Basic Science and Humanities, Indian Institute of Information Technology, 813210, Bhagalpur, India
² Department of Mathematics, Institute of Science, Banaras Hindu University, 221005, Varanasi, India
³ Department of Mathematics & Computing, Indian Institute of Technology (ISM), 826004, Dhanbad, Jharkhand, India

^d ranjit@iitism.ac.in

Received: 26 January 2022
Accepted: 5 March 2022
Published online: 19 March 2022

Abstract

In this paper, we investigate a mathematical model of plankton dynamics in an aquatic system. We consider the fact that phytoplankton take refuge and release toxic chemicals to reduce their predation by the zooplankton who is assumed to be a generalist predator. We make the system more realistic with the inclusion of seasonal variations of the model parameters representing input of nutrients, refuge taken by phytoplankton, toxins released by phytoplankton and supply of additional foods for zooplankton. The autonomous and nonautonomous systems are analyzed mathematically, and numerical simulations explore various dynamics of both the systems. In the absence of seasonal forcing, we observe that the system destabilizes on a gradual increase in the input rate of nutrients and recycling of dead biomass of phytoplankton into nutrients concentration. In contrast, refuge taken by phytoplankton, toxins liberation by phytoplankton and intraspecific competition among the species of phytoplankton have potentials to terminate the persistent oscillations, and bring stability in the ecosystem. Supply of additional foods to zooplankton in low (high) quantity creates instability (stability) in the planktonic system. Moreover, in the presence of seasonal forcing, we observe different dynamical features including periodic solution, higher periodic solutions, bursting patterns and boundary periodic solution. Overall, our findings not only provide insights about the sustainability of biodiversity by potentially explaining the emergence of seasonally recurring planktonic blooms, but also could be employed to assist develop management strategies to preserve and restore the integrity of an aquatic habitat.