Volterra-Gegenbauer Modeling of Nonlinear Systems for Global Fishery Availability Under Anthropogenic Stress

This study introduces the Volterra–Gegenbauer model, based on convergent approximation theory, for effectively representing nonlinear dynamical systems from limited data. The model uses a second-order Volterra series, approximating its kernels (which capture the system’s nonlinearities) with an orthogonal finite basis of Gegenbauer polynomials. Furthermore, optimizing the Gegenbauer parameters allows for adjustable complexity, ensuring that the model captures low-frequency nonlinear variations while preventing overfitting. The model was applied to analyze the dynamics of global fisheries impacted by marine habitat degradation, using anthropogenic variables such as ocean acidification, CO2 emissions, ocean heat content, and global temperature anomalies. Despite being based on a limited 74-year dataset, the model achieved a robust fit, with a mean relative error of 1.617%. This accuracy confirms the model’s ability to describe the nonlinear trend of ecosystem decline. Ultimately, this work provides a mathematically adaptable tool for modeling nonlinear systems in control applications with limited data. Finally, the study highlights the need to address the rapid ecological collapse of marine habitats.