Stability Analysis on Mangrove Forest Resource Models with Proboscis Monkey and Fish Pond Land Interaction with Time Delay

Abstract

Abstract Mangrove is one of the most important ecosystems in Balikpapan, where the Proboscis monkeys-an endemic animal in Borneo-lives. The growth of their population is affected by the opening of pond land by human around the forest. In this research, the problem from the interaction among the growth rate of mangrove, monkey and the opened pond land is presented in a mathematics model in the form of prey-predator for those three variables. We give an attention to the model by introducing time delays for the growth rate of fish pond land. It shows that the linearized system performs a small perturbation and the value of critical delay of the characteristic equation will affects the stability of the equilibrium point and causes stability changes (Hopf bifurcation). In this work, we obtain the existence of a critical value of the time delay and the fulfillment of the transversal conditions.