Dynamics analysis of a generalized stochastic predator-prey model based on DD-RBFNN algorithm

Jing-Yan Qi, Yong-Feng Guo and Qian-Qian Wang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 880-899

Abstract: The Fokker Planck Kolmogorov (FPK) equation stands as an indispensable instrument for the stochastic analysis of predator-prey systems, facilitating the conversion of probabilistic challenges into deterministic formulations. We propose the Data-Driven Radial Basis Function Neural Network (DD-RBFNN) algorithm to solve the FPK equations, which can be obtained via a generalized two-dimensional predator-prey system with multiplicative Gaussian white noise excitations, for scrutinizing the corresponding stochastic characteristics. The key innovation of this study lies in addressing the inherent non-negativity constraint of predator-prey models that complicates target domain determination, achieved through the modification made to the conventional RBFNN algorithm. To circumvent the trial-and-error costs, optimize computational costs and enhance overall computational efficiency, we introduce a novel method for delineating the target domain for the training dataset and use the number theoretical method (NTM) for the selection of training points. Precision and effectiveness are corroborated through a series of numerical examples that vary in functional nutritional functions. Moreover, the semi-analytical solutions derived from the DD-RBFNN algorithm exhibit a superior degree of smoothness when contrasted with the numerical solutions yielded by the Monte-Carlo Simulation (MCS) or the fourth-order Runge-Kutta algorithm.

Keywords: Radial Basis Function Neural Network; Predator-prey system; Fokker Planck Kolmogorov equation; Gaussian white noise (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:880-899

DOI: 10.1016/j.matcom.2025.08.009

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