Analysis of Mangrove Forest Resource Depletion Models due to The Opening of Fish Pond Land with Time Delay

Mangrove forest is an ecosystem with many resources and high biological diversity that contain many species of animal, such as proboscis monkeys. One of the problems that keep happening on mangrove forest is the opening of fish pond. Opening of fish pond can damage mangrove resource by the degradation of the mangrove habitat. This study aims to analyze the depletion stability model of mangrove forest resources with time delay, and to show effect of time delay and the presence of change in the equilibrium point (Hopf bifurcation) on depletion stability model of mangrove forest resources due to fish pond openings. The depletion stability model of mangrove forest resources can be modeled as a system of nonlinear differential equations. In the numerical simulation results, critical value of delay (τ0) is 7.05 and the transverse conditions are not fulfilled. This mean there is no change in stability and the delay time parameter (τ) does not affect the stability of the system. System will remain stable when the mangrove forests, proboscis monkeys, and fish ponds are in equilibrium. In other words, mangrove forests, proboscis monkeys, and fish ponds can coexist even though time delays, and the analysis using the Hopf bifurcation cannot be carried out

OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES

Energy has a very important role in everyday life. Dependence on non-renewable energy increases its vulnerability to supply instability, making it important to seek alternative energy sources to overcome this dependence. Bioenergy is an alternative energy produced from organic materials such as biomass. Control of renewable energy is needed to increase production and empowerment. In this research, a mathematical model of biogas production growth in the form of differential equations formed with optimal control modifications is proposed. Completion of the model is carried out by forming an objective function, as well as determining the Hamilton function and Lagrange function. Numerical simulations in the model show that providing control can increase biogas production as a sustainable energy source