A stochastic differential game approach toward animal migration

摘要: A stochastic differential game model for animal migration between two habitats under uncertain environment, a new population dynamics model, is formulated. Its novelty the use of an impulse control formalism to naturally describe migrations with different timings and magnitudes that conventional models could not handle. Uncertainty environment faces formulated in context multiplier robust control. The optimal strategy give maximized minimal profit found through Hamilton–Jacobi–Bellman quasi-variational inequality (HJBQVI). key message from HJBQVI its free boundary determines strategy. Solving carried out specialized stable convergent finite difference scheme. This paper theoretically suggests sub-additivity performance index, index be optimized migration, critically affects resulting computational results established scheme are consistent theoretical predictions support importance property. Social interaction reduce net mortality rate also quantified, suggesting linkage present existing models.