Spatiotemporal Dynamics of a Plankton System: Impacts of Phytoplankton Refuge and Supplementary Food for Zooplankton

This investigation delves into the intricate dynamics of a plankton system within an aquatic reservoir. Notably, the phytoplankton possesses the refuge-seeking behavior and releases bioactive compounds, thereby attenuating the grazing pressure imposed by zooplankton. Concurrently, zooplankton growth depends on phytoplankton and is also supplemented by additional nutritional sources. We also investigate the dynamics of the corresponding diffusive system. Employing rigorous mathematical and numerical methodologies, we scrutinize both temporal and spatiotemporal models. We calibrate the proposed model using field data collected from Talsari and Digha Mohana, India, and estimate key parameters to align with the patterns observed in the real data. Numerical simulations elucidate a spectrum of bifurcations, encompassing Hopf, transcritical, saddle-node, Bautin, and Bogdanov–Takens bifurcations. The parameter space, encompassing the growth rate of phytoplankton, refuge level of phytoplankton, rate of toxins released by phytoplankton, and zooplankton growth due to supplementary food, is found to exert profound effects on system behavior. Furthermore, our investigation delves into the influence of diffusion coefficients of zooplankton, phytoplankton refuge, and the growth rate of zooplankton in response to additional food sources, on the spatial distribution of plankton densities. The spatial model elucidates distinctive patterns, manifesting as circular and spot-like configurations. Furthermore, our study examines the impact of environmental white noise on system dynamics by introducing stochastic elements. We explore noise-induced transitions between equilibria within the tri-bistable region. Utilizing stochastic sensitivity functions, we analyze stochastic properties, construct confidence ellipses, and estimate noise intensity thresholds for state transitions. These findings offer valuable insights into the complex dynamics of plankton systems influenced by a refuge-seeking behavior of phytoplankton and supplementary nutrition for zooplankton.