Continuous Description of Discrete Biological Data

Abstract

The applicability of differential equations to description of integer values dynamics in bio-informatics is investigated. It is shown that a differential model may be interpreted as a continuous analogue of a stochastic flow. The method of construction of a quasi-Poisson flow on the base of multi-dimension differential equations is proposed. Mathematical correctness of the algorithm is proven. The system has been studied by a computer simulation and a discrete nature of processes has been taken into account. The proposed schema has been applied to the classical Volterra's models, which are widely used for description of biological systems. It has been demonstrated that although behaviour of discrete and continuous models is similar, some essential qualitative and quantitative differences in their dynamics take place.