JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (10): 74-88.doi: 10.6040/j.issn.1671-9352.0.2023.547

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Stationary distribution and probability density function of a stochastic predation system

ZHAO Yufeng1, LIU Guirong2   

  1. 1. School of Computer Science and Information Engineering, Shanxi Technology and Business College, Taiyuan 030006, Shanxi, China;
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030000, Shanxi, China
  • Published:2024-10-10

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Abstract: A class of stochastic predator-prey models with predator-stage structure and rate-dependent Holling III type functional responses are developed. Firstly, the existence and uniqueness of global positive solutions for stochastic model are obtained. Secondly, the existence and uniqueness of the ergodic stationary distribution are studied by constructing a suitable Lyapunov function and using the ergodic theory of Has'Minskii. Next, by solving the corresponding three-dimensional Fokker-Planck equation, the exact expression of the probability density function of the stochastic predator-prey model near the positive equilibrium point is derived. Finally, the rationality of the theoretical results is verified by numerical simulation.

Key words: stochastic predator-prey model, stationary distribution, stage structure, ratio-dependent, probability density function

CLC Number: 

  • O175
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