Triple modeling scheme for optimal control related to weighted population dispersal

Abstract

In this work, a triple modeling scheme using Navier-Stokes, Convection Diffusion, and Stochastic Differential Equations, (NSEs, CDEs, and SDEs), is established in the context of population dispersal. An initial model is motivated through the Langrangian viewpoint expressed by the SDEs. The consequent Eularian approach is considered in an advective indefinitely weighted periodic parabolic setup. Weight and drift effects on the CDE prototype principal eigenvalue are established. The second leg in this modeling scheme lies in applying the Hopf-Cole transform to CDEs, showing that resulting NSEs hide a great potential for interpreting velocity fields in population dispersal dynamics.