Stochastic Analysis of Predator–Prey Models under Combined Gaussian and Poisson White Noise via Stochastic Averaging Method
| Autor: | Rongchun Hu, Yong Xu, Dongxi Li, Wantao Jia |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Stochastic modelling
statistical responses Science QC1-999 Gaussian Population Monte Carlo method combined Gaussian and Poisson white noise General Physics and Astronomy Astrophysics Noise (electronics) Article predator competition symbols.namesake Quantitative Biology::Populations and Evolution Statistical physics education Mathematics education.field_of_study stationary PDF Stationary distribution Stochastic process Physics White noise stochastic averaging method QB460-466 symbols predator saturation |
| Zdroj: | Entropy, Vol 23, Iss 1208, p 1208 (2021) Entropy Volume 23 Issue 9 |
| ISSN: | 1099-4300 |
| DOI: | 10.3390/e23091208 |
| Popis: | In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results. |
| Databáze: | OpenAIRE |
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