Optimal Control Theory Applied to a Class of Biological Population Growth Models

adjoint age distribution assume bang-bang control behavior birth and death birth rate boundary value problem constant constraints control is considered control model control problem convergence cost of control death rates density discussed dynamic programming Ecology effect equations 2.23 exp(x factors Gause model given Huffaker Imax increase initial conditions interval invariant imbedding K₁ K₂ lation linear problem Lmax logistic curve Lotka Lotka-Volterra System Cost Mathematical maximum principle N₁ N₂ non-linear boundary value number of prey obtain Optimal Control Applied optimal control theory optimal process optimization problem P₁ p₁(t P₂ pest phase plane point boundary value Pontryagin Maximum Principle popu population dynamics population growth Population Model predator predict projection matrix Quasi-linearization R₁ R₂ rate per individual Riccati equation Ru dt shooting methods simple model situation solution solve species population species system Statistical Mechanics survival rates sweep method technique terminal conditions total number vector Volterra