Stability and control in the predator population

The large population of the spruce budworm (predator) can cause significant change in the fir trees. Several strategies have been used in Canada and North America to reduce the spruce budworm (predator) population. In this work, we consider the spruce budworm population model originally created by Ludwig et al. in 1978. We introduce stability techniques to analyze the dynamical behavior of the spruce budworm population and find the equilibrium position and global stability. Then we use optimal control techniques to control the spruce budworm population and present numerical simulations by using Runge-Kutta fourth scheme. Our techniques should be useful to model the dynamics of other predators with physiological structures.