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<p>Stochastic predator–prey systems with Beddington–DeAngelis (BD) functional response provide a biologically realistic framework for modeling population dynamics under random influences. When stochastic fluctuations are introduced through state-dependent noise, the resulting stochastic differential equations (SDEs) exhibit different long-term behaviors depending on the parameter relationships. Numerical simulation of such systems poses significant challenges: standard schemes often fail due to the nonlinear drift structure, violation of global Lipschitz conditions, and instability in long-term integration. In this work, we develop a numerical method tailored for the long-term simulation of this type of system. The approach is based on a transformation of the original SDE into a random differential equation (RDE), which allows the use of stable exponential integrators. The resulting approximation is then transformed back to recover the trajectories of the original SDE. Numerical experiments demonstrate that the proposed method significantly outperforms commonly used standard schemes in both stability and accuracy. In particular, it reliably reproduces qualitative dynamical features predicted by theory, even over long time horizons.</p>

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Long-term simulation of stochastic predator–prey systems with Beddington–DeAngelis functional response

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • H. de la Cruz,
  • M. Muñoz

摘要

Stochastic predator–prey systems with Beddington–DeAngelis (BD) functional response provide a biologically realistic framework for modeling population dynamics under random influences. When stochastic fluctuations are introduced through state-dependent noise, the resulting stochastic differential equations (SDEs) exhibit different long-term behaviors depending on the parameter relationships. Numerical simulation of such systems poses significant challenges: standard schemes often fail due to the nonlinear drift structure, violation of global Lipschitz conditions, and instability in long-term integration. In this work, we develop a numerical method tailored for the long-term simulation of this type of system. The approach is based on a transformation of the original SDE into a random differential equation (RDE), which allows the use of stable exponential integrators. The resulting approximation is then transformed back to recover the trajectories of the original SDE. Numerical experiments demonstrate that the proposed method significantly outperforms commonly used standard schemes in both stability and accuracy. In particular, it reliably reproduces qualitative dynamical features predicted by theory, even over long time horizons.