Agriculture and mining get interlinked with each other when they take place concurrently in rural parts of the world. In order to explore it in mathematical terms, a nonlinear dynamical model system is proposed in this study with agricultural yield, human population and mining as system variables. The agricultural yield is assumed to have logistic growth and also, supplements rural human population growth. Mining is assumed to be not only advancing with constant rate, but also getting induced through rural human population. The model is qualitatively analyzed for the identification of different equilibrium states and their stability behaviors. The model analysis reveals the conditions under which agriculture and mining together with rural population can achieve a stable system. These qualitative findings are substantiated with quantitative results, under which sensitiveness of different parameters of the model towards the model outcomes are investigated through global sensitivity analysis technique. Also, bifurcation parameters and their critical values are determined to predict the states of qualitative behavioral change. The results suggest that a balanced system can be obtained by taking measures to control unconducive mining and augment agricultural outputs.

中文翻译：

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农村农矿共存非线性动力学模型的数学分析与数值模拟

当农业和采矿业同时发生在世界农村地区时，它们就相互关联了。为了在数学上对其进行探索，本研究提出了一个以农业产量、人口和采矿为系统变量的非线性动力学模型系统。假设农业产量具有后勤增长，并且补充了农村人口增长。假设采矿不仅以恒定的速度发展，而且还通过农村人口得到诱导。对模型进行定性分析，以识别不同的平衡状态及其稳定性行为。模型分析揭示了农业和采矿业与农村人口共同实现稳定系统的条件。这些定性发现得到定量结果的证实，通过全局敏感性分析技术研究模型不同参数对模型结果的敏感性。此外，确定分岔参数及其临界值以预测定性行为变化的状态。结果表明，通过采取措施控制不良采矿和增加农业产量，可以获得平衡的系统。