A common description of the deterministic and stochastic models

2 A common description of the deterministic and stochastic models Formal components and formal elementary reactions 

The formal chemical components of the model are as shown in Table 7.1. 

a short description of the deterministic model is given. 

The deterministic model is the (nonautonomous, nonpolynomial) induced kinetic differential equation of the reactions in Fig. 7.13. This model was described in detail by Herodek et al. (1982). Now we give a formal description of a small part of the model. As an example let us consider the time evolution of summer phytoplankton. Our assumption is that it takes part in the elementary reactions No. 2, 6, 13, 26, 34, therefore the equation for is  

PM AX corresponds to the reaction rate constant, called maximal production rate in the present context, TEMP expresses a kind of dependence on time through temperature (a phenomenon common in nonisothermal reactions), it is called here temperature limitation, Iq is an external forcing function it is the global radiation on the water surface, U2 is a joint limitation factor describing light- and nutrient-dependence of primary production, or to use the language of reaction kinetics it expresses the deviation from mass-action type kinetics. 

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