{"title":"冰川可持续生态旅游动态模型的稳定性分析","authors":"Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen","doi":"10.1016/j.rinam.2025.100636","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> based on the carbon-temperature equilibrium and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100636"},"PeriodicalIF":1.3000,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability analysis of a dynamical model for sustainable Glacier ecotourism\",\"authors\":\"Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen\",\"doi\":\"10.1016/j.rinam.2025.100636\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> based on the carbon-temperature equilibrium and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.</div></div>\",\"PeriodicalId\":36918,\"journal\":{\"name\":\"Results in Applied Mathematics\",\"volume\":\"27 \",\"pages\":\"Article 100636\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2590037425001001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037425001001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Stability analysis of a dynamical model for sustainable Glacier ecotourism
In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate based on the carbon-temperature equilibrium and based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when and , and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both and . Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.
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