Probabilistic Analysis of a Marine Ecological System with Intense Variability

Abstract

This work seeks to simulate and examine the complex character of marine predation. By taking into account the interaction between phytoplankton and zooplankton, we present a sophisticated mathematical system with a general functional response describing the ecological competition. This system is disturbed by a novel category of perturbations in the hybrid form which simulates certain unstable climatic and environmental variations. We merge between the higher-order white noise and quadratic jumps to offer an excellent overview of the complexity induced in the ecosystem. Analytically, we offer a surrogate framework to get the sharp sill between stationarity and zooplankton eradication. Our analysis enriches and improves many works by proposing an unfamiliar form of perturbation and unifying the criteria of said asymptotic characteristics. Numerically, we probe the rigor of our sill in a non-standard case: cubic white noise and quadratic leaps. We demonstrate that the increased order of perturbation has a significant effect on the zooplankton living time. This result shows that the sources of intricate fluctuations carry out an active role in the transient dynamics of marine ecological systems.