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

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

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.

Suggested Citation

  • Qi, Jing-Yan & Guo, Yong-Feng & Wang, Qian-Qian, 2026. "Dynamics analysis of a generalized stochastic predator-prey model based on DD-RBFNN algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 880-899.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:880-899
    DOI: 10.1016/j.matcom.2025.08.009
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    References listed on IDEAS

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    1. Qiu, Hong & Deng, Wenmin, 2018. "Optimal harvesting of a stochastic delay tri-trophic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1715-1728.
    2. Zhuo, Xiao-jing & Guo, Yong-feng & Qi, Jing-yan & Wang, Qian-qian, 2024. "Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    3. Han, Qun & Xu, Wei & Hu, Bing & Huang, Dongmei & Sun, Jian-Qiao, 2018. "Extinction time of a stochastic predator–prey model by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 351-366.
    4. Liang, Yanming & Guo, Yongfeng & Lin, Zifei, 2024. "Using reservoir computing to solve FPK equations for stochastic dynamical systems under Gaussian or Non-Gaussian excitation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 645-662.
    5. Xue, Yalong, 2024. "Impact of both-density-dependent fear effect in a Leslie–Gower predator–prey model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
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