Management and Analysis of Biological PopulationsManagement and Analysis of Biological Populations ... |
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admissible set analysis AV(N c₁ c₂ compute constraint control variable costate equations density diagonal matrix difference equation differential equations drive the system ecology ecosystem model eigenvalues Example exists a positive feedback control policy finite fish population fishery follows function V(N global minimum globally stable harvesting policy Hence implies initial intraspecific interactions isoclines Liapunov function Liapunov-like function limit cycle linear logistic model Lotka-Volterra model maximum multispecies N₁ N₂ natural dynamics negative definite nonlinear nonnegative equilibrium optimal control problem optimal feedback optimal policy optimal size limit orthant p₁ p₂ parameters patch perturbations population models positive constants positive diagonal matrix positive equilibrium positive number positive orthant predator prey prey-predator system region of ultimate satisfies sector stable single-species population singular control singular solution species suitable Liapunov function Suppose switching Theorem theoretical ecology trajectory two-species u₁ u₂ ultimate confinement unstable values vector X₁ year-class