{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T03:36:38Z","timestamp":1777520198485,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T00:00:00Z","timestamp":1519344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Nature Science Foundation of China","award":["11502199"],"award-info":[{"award-number":["11502199"]}]},{"name":"the National Nature Science Foundation of China","award":["11402157"],"award-info":[{"award-number":["11402157"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method.<\/jats:p>","DOI":"10.3390\/e20020143","type":"journal-article","created":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T11:31:36Z","timestamp":1519385496000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation"],"prefix":"10.3390","volume":"20","author":[{"given":"Wantao","family":"Jia","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongxi","family":"Li","sequence":"additional","affiliation":[{"name":"College of Big Data Science, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,23]]},"reference":[{"key":"ref_1","first-page":"887","article-title":"Stability and complexity in model ecosystems","volume":"44","author":"May","year":"1977","journal-title":"IEEE Trans. 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