Some probable characteristices of "beast-sacrifice"
system in stochastic medium
O.V. Muzychuk
N. Novgorod Arch.and Civ.Eng.Acad., Russia
One from the classical problems of non-linear dynamics is the interaction of self-regulated communities "beast-sacrifice" form. However in reality parameters of the environment medium subjected to the action of random factors and this problem becomes a stochastic one. Such stochastic systems are usualy investigated using Fokker-Planck equations and the aparatus of diffusian-type processes. As we know, some analytic rezults are obtained only for one delta-correlated parametric fluctuation case. In the real situation there are several random parameters and delta-correlated approcsimation of them may be unsuitable.
Approximation of parameters fluctuations by "telegraph-type" random processers makes possability to consider the influence of there correlation scale for the statistical characteristics. (This representation is according to well-known in linear theory Bourret approximation). This way succeedes to obtain mean and root-mean-square values of interacting populations. More detail description one can do linearising the initial stochastic equations near the balance states. It makes possability to inverstigate the influense of the intensity and spectrum form of fluctuations on the required quantities. For the limiting situation of existence only "sacrifice" population (we have well-known Ferhulst equation) one can find the probable density of population numbers and investigate the process of relaxation for main probable characteristics.