Stability analysis of mangrove forest resource depletion models due to the opening of fish pond land

Abstract

The existence of Mangrove Forest is very necessary for the cycle of the food chain of marine fauna and its ecosystem. Balikpapan City has several Mangrove forest conservation areas that contain some rare – protected species. In this paper, a mathematical model is formulated to examine the problem of decreasing Mangrove forest resources due to the population of Bekantan (Nasalis larvatus), and the land clearing for fish ponds in the area of Mangrove forest conservation areas. The cumulative density of Mangrove forest resources and density of Bekantan (Nasalis larvatus) are assumed to follow the logistic model with predator-prey types of non-linear interactions. The main focus of this paper is to develop a Mangrove forest model derived from assumptions on the forest resource model and direct observation in the Mangrove Graha Indah forest conservation area of Balikpapan city. Furthermore, the model was analyzed using the stability theory of differential equations and numerical simulations to obtain an illustration that the cumulative density of Mangrove forest resources and Bekantan (Nasalis larvatus) would be significantly decreased if the land clearing for fishponds was not controlled.