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We consider a size-structured aggregation and growth model of phytoplanktoncommunity proposed by Ackleh and Fitzpatrick [2]. The model accounts for basicbiological phenomena in phytoplankton community such as growth, gravitationalsedimentation, predation by zooplankton, fecundity, and aggregation. Ourprimary goal in this paper is to investigate the long-term behavior of theproposed aggregation and growth model. Particularly, using the well-knownprinciple of linearized stability and semigroup compactness arguments, weprovide sufficient conditions for local exponential asymptotic stability ofzero solution as well as sufficient conditions for instability. We expressthese conditions in the form of an easy to compute characteristic function,which depends on the functional relationship between growth, sedimentation andfecundity. Our results can be used to predict long-term phytoplankton dynamic

Criteria for linearized stability for a size-structured population model