Genocchi Polynomials in Volterra Model to Identify Non-Linear Systems, Case of World Ocean Fishery

This study aims to model non-linear systems by Genocchi polynomials and the Volterra series as approximation functions of dynamic systems. So, expressing the Volterra kernels by Genocchi Polynomials represents the cornerstone of the study to obtain models without involving huge parameter numbers. Moreover, results show the fast convergent approximation of this model gives a helpful characteristic for systems identification, mainly on systems noisy data and reduced-time-interval dynamic. The Genocchi polynomials and the Volterra model studied the ocean fishery as proof of the technique. Using the pH index of ocean water, the global temperature anomaly, the carbon dioxide emission, and the ocean heat content as independent variables, the math model provides forecasts for world ocean fishery with an error of less than 2.5% for the last fifty years. The results, reveal model robustness, for this identification technique is a reliable proposal modeling non-linear systems.