Design of a fractional-order environmental toxin-plankton system in aquatic ecosystems: A novel machine predictive expedition with nonlinear autoregressive neuroarchitectures
Muhammad Junaid Ali Asif Raja, Adil Sultan, Chuan‐Yu Chang, Chi‐Min Shu, Muhammad Shoaib, Adiqa Kausar Kiani, Muhammad Asif Zahoor Raja
Abstract
Artificial intelligence has transformed both plankton dynamics and hazardous material management under toxic environments by enhanced hazard prediction in detecting how toxins affect plankton population and potentially uncovering greater depth of ecological insights. In proposed study, nonlinear autoregressive exogenous neural network coupled with Levenberg-Marquardt is efficaciously selected to model fractional order toxin plankton (FOTP) system asserting the phytoplankton and zooplankton dynamics in aquatic environment under influence of environmental toxins. The fractional differential ecological TP system incorporates density population of phytoplankton, zooplankton and environmental toxins exacted by fractional Adams multistep predictor-corrector method across arbitrary fractional order cases varying intrinsic growth rates of phytoplankton and zooplankton, zooplankton carrying capacity, phytoplankton toxin release, fish predation parameters (half-saturation constant and maximum rate), environmental toxin depletion, and dynamic phytoplankton carrying capacity. Synthetic datasets were split into training, testing, and validation subsets to model the FOTP system using an intelligent neurocomputing paradigm. The proficiency of the selected neural networks is demonstrated by performance metrics—MSE convergence, time-series fitness patterns, regression reports, error histograms and correlation analyses—while comparative analysis with numerical outcomes and absolute error plots underscores the robustness and stability of the neurocomputing architecture. Rigorous analysis on single step and multistep ahead predictors with error of order 10 −5 further highlights the efficacy of employed neurocomputing design for optimal and precise forecasting of intricate FOTP system dynamics. This study demonstrates that intelligent computing can effectively forecast FOTP dynamics and serve as a framework for addressing aquatic ecological hazards.