Aggregation on a Toroidal Domain of the Random Walk Systems Based on a Record Function

In previous papers by Oprisan et al. the evolution of stochastic systems based on the record function was studied. The present study concerning this problem shows that the boundary conditions which appear in the system have an influence on the aggregation velocity only. Such a system, omitting these boundary conditions is studied. This is done by closing the environment into a toroidal one and studying the behavior of the system which is influenced only by the record function. We use the same record function as in a previous Letter [D. Amarie, S.A. Oprisan, M. Ignat, Phys. Lett. A 254 (1999) 112]. A new method of system aggregation analysis is introduced here. Theoretical arguments and numerical simulation supporting this idea are presented.