Abstract
The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.
Highlights
The focus of the study in this paper is to model deforestation due to population density and industrialization
The equalibrium point of disturbance-free is defined as a condition where there is no damage to forest resources caused by population density and industrialization density
The equilibrium point T E2(x, y, z) shows that the rate of forest resources has not changed, there is an effect of population density on the system with the condition L(p + s) > 0, without being influenced by the existence of industrialization
Summary
The focus of the study in this paper is to model deforestation due to population density and industrialization. In the compartment of forest destruction and population density it is assumed that it grows continuously in the form of a logistical equation by considering the natural damage to forest resources and the presence of migration factors that cause an increase in population.
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