MATHEMATICAL ANALYSIS AND NUMERICAL SIMULATION OF A NONLINEAR DYNAMICAL MODEL FOR THE COEXISTENCE OF AGRICULTURE AND MINING IN RURAL AREAS

Abstract

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.