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• W128641344 abstract "Identification of conditions of ecosystem stability and stable populations coexistence is a problem of highest importance in mathematical ecology. It is usually studied under specific assumptions made regarding the functional form of nonlinear feedbacks. Apparently, such an approach is lacking generality. In this paper, we consider a chemostat-type model of the phytoplankton-nutrient interaction, which can be regarded as a simple ecosystem model, in a general case. The plankton growth/nutrient uptake rate is described by an unspecified function of two variables (i.e., of the nutrient concentration N and the plankton density P) and the plankton mortality is an arbitrary function of P. We provide a rigorous mathematical consideration of the global properties of this system and derive the conditions that ensure existence and uniqueness of a globally asymptotically stable equilibrium state. Interestingly, these conditions correspond to much weaker constraints on the plankton growth rate properties than monotonicity and non-convexity that are usually assumed. We also identify a parameter that allows us to distinguish between existence and non-existence of the steady stable plankton-abundant state." @default.
• W128641344 created "2016-06-24" @default.
• W128641344 creator A5074037128 @default.
• W128641344 creator A5084425820 @default.
• W128641344 date "2008-03-03" @default.
• W128641344 modified "2023-09-25" @default.
• W128641344 title "Toward a General Theory of Ecosystem Stability: Plankton-Nutrient Interaction as a Paradigm" @default.
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• W128641344 doi "https://doi.org/10.1007/978-3-7643-8591-0_2" @default.
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