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We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational sedimentation, predation by zooplankton, fecundity, and aggregation. Our primary goal in this paper is to investigate the long-term behavior of the proposed aggregation and growth model. Particularly, using the well-known principle of linearized stability and semigroup compactness arguments, we provide sufficient conditions for local exponential asymptotic stability of zero solution as well as sufficient conditions for instability. We express these conditions in the form of an easy to compute characteristic function, which depends on the functional relationship between growth, sedimentation and fecundity. Our results can be used to predict long-term phytoplankton dynamic
We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equ
Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general evolution eq
This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population dynamics mo
In the present paper we analyze the linear stability of a hierarchical size-structured population model where the vital rates (mortality, fertility and growth rate) depend both on size and a general functional of the population density (environment).
In this paper we consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference schemes are developed to approximate the solution of the mathematical mod