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Coupled nonlinear stochastic integral equations in the general form of the predator-prey model

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  • Tamimi, Hengameh
  • Ghaemi, Mohammad Bagher
  • Saadati, Reza

Abstract

This article explores the stochastic predator-prey model. This model offers a probabilistic framework for understanding the dynamics of interacting species. The stochastic predator-prey model is a practical tool for predicting the intricate balance of survival between predators and their prey in the face of nature's unpredictability. This study introduces a new measure of noncompactness and applies it to investigate solutions in nonlinear stochastic equations. Additionally, we present a numerical method using block pulse functions and demonstrate its convergence through the new measure of noncompactness for solving the system of stochastic integrals. Finally, the proposed method is employed to solve a numerical example.

Suggested Citation

  • Tamimi, Hengameh & Ghaemi, Mohammad Bagher & Saadati, Reza, 2025. "Coupled nonlinear stochastic integral equations in the general form of the predator-prey model," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005848
    DOI: 10.1016/j.amc.2024.129123
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    References listed on IDEAS

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    1. Balasubramaniam, P., 2022. "Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Joseph P. Noonan & Henry M. Polchlopek, 1991. "An Arzela-Ascoli type theorem for random functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-8, January.
    3. K. Maleknejad & H. Safdari & M. Nouri, 2011. "Numerical solution of an integral equations system of the first kind by using an operational matrix with block pulse functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 195-199.
    4. Kazemi, M. & Yaghoobnia, A.R., 2022. "Application of fixed point theorem to solvability of functional stochastic integral equations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
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