Sistem Dinamik Model Pengurangan Biomassa Hutan Akibat Penumpukan Industrialisasi

Abstract

Forests are lungs of the earth which regulate ecological stability and it is important in cycles of oxygen (O2) and carbon dioxide (CO2). Forests give many benefits for supporting human life. The sustainability of forests for life of human are determined by consciousness of society in using them. Uncontrolled exploitations have effects for depletion of forest biomass. In this research, we present a nonlinear mathematical model, which has been analyzed to study the depletion of forest biomass. Moreover, this research also considers the implication of crowding by industrialization on forest biomass. A mathematical model is formulated to investigate the depletion of forest biomass. There are four variabels to consider, namely, the density of forest biomass (��), population of human (��), population pressure (��), and density of industrialization (��). In this research, we get four nonnegative equilibria, namely, ��1, ��2, ��3, and ��4. The equilibria ��1, ��2, and ��3 are analyzed by linierizing the system. Then, we determine the eigenvalues of the Jacobian matrix for those equilibria. The equilibrium ��4 is analyzed by use stability theory of Liapunov. The analysis of the model showed that under certain condition, ��1, ��2, and ��3 are unstable saddle point. Whereas the equilibrium ��4 is globaly asymtotically stable. The numerical simulations show that the equilibrium level of forest biomass density decrease as the equilibrium level of the human population, population pressure, and density of industrialization increase. It is lower than its original carrying capacity. Moreover, if the rate of crowding by industrialization increases, then the forest biomass density decreases. In all simulations, we conclude that if conditions of stability theorems are satisfied, then dynamics of the system always attain their corresponding equilibrium level.