Seasonal Stochasticity Drives Phytoplankton–Zooplankton Dynamics

In this study, we examine a deterministic model incorporating refuge, additional food sources, and toxins. The existence and stability of positive equilibria and the bifurcation analyses are discussed. Our numerical outcomes entail that increased zooplankton growth due to additional food leads to the disappearance of phytoplankton species, while a significant drop in nutrient levels results in zooplankton extinction within the ecosystem. Notably, the refuge by phytoplankton has a tendency to terminate the persistent oscillations and stabilize the system. As seasonal stochasticity significantly influences the dynamics of planktonic system, so we introduce seasonality into environmental noise and certain model parameters. In this case, we analyze both the regularity and the dichotomy between persistence and extinction. The numerical evidences demonstrate periodic solutions, strong/weak persistence, and plankton extinctions resulting from stochasticity and/or seasonality. Furthermore, the seasonally forced noise, intriguingly, has the capacity to exert control over hyperchaos, yielding a distinctive pattern in plankton populations.