One-Step Stochastic Processes Simulation Software Package

It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic models. Authors have improved the method of stochastic models construction for the class of one-step processes and illustrated by models of population dynamics. Population dynamics was chosen for study because its deterministic models were sufficiently well explored that allows to compare the results with already known ones. To optimize the models creation as much as possible some routine operations should be automated. In this case, the process of drawing up the model equations can be algorithmized and implemented in the computer algebra system. Furthermore, on the basis of these results a set of programs for numerical experiment can be obtained. The computer algebra system Axiom is used for analytical calculations implementation. To perform the numerical experiment FORTRAN and Julia languages are used. The Runge- Kutta method for stochastic differential equations is used as numerical method. The program complex for creating stochastic one-step processes models is constructed. Its application is illustrated by the predator-prey population dynamic system. Computer algebra systems are very convenient for the purposes of rapid prototyping in mathematical models design and analysis.

stochastic differential equations, “predator-prey” model, master equation, Fokker-Planck equation, computer algebra software, Axiom system