Stability analysis of palm oil control model with felling effect
Keywords:
Stability Analysis, Logistic Equation, Palm Oil Plantation, Ordinary Differential Equation, Optimal Control ModelAbstract
The stability analysis of logistic growth model is a norm in plantation and eco-biological environment. It can be ecologically stable and sustained in a long run. However, any additional variation to the model may fluctuate the economy over time. An optimal control felling rate model was successfully created for palm oil plantation based on the logistic growth model. The model can do well in representing the plantation but the stability is not yet analysed, mainly due to the presence of felling rate as the new added criterion. This study analysed the stability of equilibrium point of the optimal control felling rate model. The equilibrium points were identified and the small perturbation around the equilibrium points was geometrically computed. The analysis of small perturbation of felling rate showing equilibrium point decay exponentially indicates that the model was ecologically stable with the presence of control felling rate. The trajectories of palm oil biomass versus time verified the stability of equilibrium points with the presence of felling rate.
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