\R × BL^* Valued Consumer Resource Model

2014/12/01 by Cleveland, John
#91A22 34G20 37C25 92D25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.0566

Abstract

The ideas and techniques developed in \citeCLEVACK, JC2 are applied to the basic pure selection (no mutation) parametric heterogeneous consumer resource model developed in \citeSmithThieme to derive a fully nonlinear resource dependent selection mutation \R × BL^* valued model. Where BL^* is the dual of the Lipschitz maps, a Banach Space. By the appropriate choice of initial condition, and mutation kernel parameter this model unifies both discrete and continuous, pure selection and mutation selection, measure valued and density valued basic consumer resource models. In this paper well-posedness and uniform eventual boundedness under biologically sound assumptions is presented.

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