Population model based on cells with internal dynamics - Tamošiūnaitė, Minija; Vaišnys, J. Rimas (Nonlinear Analysis: Modelling and Control, 1998)
A model of a population is constructed by bringing together individual model organisms (cells) which have explicit internal dynamics. An attempt is made to preserve analyzability of the relatively complex model by describing the nonlinear dynamics of each cell by a set of piece-wise linear equations. In the simplest case of three linear pieces, a population with inherent oscillations in the number of cells as a function of time is obtained. A proposal is made to approximate realistic internal dynamics of selected biological features by introducing the appropriate number of linear patches, and to simulate realistic populations in this way. Another extension of the model, the description of interactions between cells through released metabolites, is used to represent the situation of a chemostat.