On the dynamics of a nutrient–plankton–fish ecosystem with Caputo fractional operator

In this study, we propose a nutrient–plankton–fish interaction model in a marine environment incorporating the Caputo fractional operator to investigate the role of various parameters, such as the mortality rate of zooplankton, the maximal ingestion rate of fish, and the nutrient consumption rate by phytoplankton, in stabilizing the system. To investigate the qualitative properties of the model, the fundamental properties of its solutions and the stability of its equilibria are examined. Further, to investigate the effect of the order of the fractional derivative on system stability, we have arbitrarily chosen four values: 0.91, 0.94, 0.97, and 1. To verify the theoretical results fo the system's stability, we present numerical examples using MATLAB. The findings identify specific biological rates that contribute to system instability, providing critical information for control. Reducing zooplankton mortality, potentially through reduced pesticide use, may unintentionally disrupt population dynamics, leading to erratic fluctuations. Also, the negative relationship between fish ingestion rate and stability serves as a cautionary tale for fishery managers. Policies that actively promote high ingestion rates risk causing the entire fish population to collapse into chaotic patterns. Moreover, the fractional-order derivative approach enhances realism by accounting for memory effects, offering deeper insights into stability and resilience compared to classical integer-order models.