Stability analysis of a dynamical model for sustainable Glacier ecotourism

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2025-08-01 DOI:10.1016/j.rinam.2025.100636

Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen

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Abstract

In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate

R_{C}

based on the carbon-temperature equilibrium and

R_{N}

based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when

R_{C} < 1

and

R_{N} \leq 1

, and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both

R_{C} < 1

and

R_{N} > 1

. Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.

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冰川可持续生态旅游动态模型的稳定性分析

本文通过构建系统动力学模型，研究了环境变化下冰川生态旅游系统的可持续演化。在流行病学模型中，基于碳-温度平衡计算RC，基于复制数法计算RN，并证明了当RC<；1和RN≤1时，零平衡是全局渐近稳定的，当RC<；1和RN>；1时，相对于正平衡的误差动态是全局一致最终有界的。基于Mendenhall冰川的数据进行了实证验证，以支持理论分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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