{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T06:30:52Z","timestamp":1762929052437,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,25]],"date-time":"2024-02-25T00:00:00Z","timestamp":1708819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Water Pollution Control and Treatment Science and Technology Major Project","award":["2017ZX07101","61200082363001"],"award-info":[{"award-number":["2017ZX07101","61200082363001"]}]},{"name":"Discipline Construction Program of Huayang Zhang, Distinguished Professor of Shandong University, School of Life Sciences","award":["2017ZX07101","61200082363001"],"award-info":[{"award-number":["2017ZX07101","61200082363001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The insect predator\u2013prey system mediates several feedback mechanisms which regulate species abundance and spatial distribution. However, the spatiotemporal dynamics of such discrete systems with the refuge effect remain elusive. In this study, we analyzed a discrete Holling type II model incorporating the refuge effect using theoretical calculations and numerical simulations, and selected moths with high and low growth rates as two exemplifications. The result indicates that only the flip bifurcation opens the routes to chaos, and the system undergoes four spatiotemporally behavioral patterns (from the frozen random pattern to the defect chaotic diffusion pattern, then the competition intermittency pattern, and finally to the fully developed turbulence pattern). Furthermore, as the refuge effect increases, moths with relatively slower growth rates tend to maintain stability at relatively low densities, whereas moths with relatively faster growth rates can induce chaos and unpredictability on the population. According to the theoretical guidance of this study, the refuge effect can be adjusted to control pest populations effectively, which provides a new theoretical perspective and is a feasible tool for protecting crops.<\/jats:p>","DOI":"10.3390\/e26030196","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T06:50:23Z","timestamp":1708930223000},"page":"196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Spatiotemporal Dynamics of Insect Predator\u2013Prey System Incorporating Refuge Effect"],"prefix":"10.3390","volume":"26","author":[{"given":"Huayong","family":"Zhang","sequence":"first","affiliation":[{"name":"Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China"},{"name":"Theoretical Ecology and Engineering Ecology Research Group, School of Life Sciences, Shandong University, Qingdao 250100, China"}]},{"given":"Xiaotong","family":"Yuan","sequence":"additional","affiliation":[{"name":"Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6085-8293","authenticated-orcid":false,"given":"Hengchao","family":"Zou","sequence":"additional","affiliation":[{"name":"Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China"}]},{"given":"Lei","family":"Zhao","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Biodiversity and Organic Farming, College of Resources and Environmental Sciences, China Agricultural University, Beijing 100193, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1342-3024","authenticated-orcid":false,"given":"Zhongyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China"}]},{"given":"Fenglu","family":"Guo","sequence":"additional","affiliation":[{"name":"Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing 102206, China"}]},{"given":"Zhao","family":"Liu","sequence":"additional","affiliation":[{"name":"Theoretical Ecology and Engineering Ecology Research Group, School of Life Sciences, Shandong University, Qingdao 250100, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,25]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Environmental Effects on Insects and Their Population Dynamics","volume":"2","author":"Khaliq","year":"2014","journal-title":"J. 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