V. Zhuravlev, P. Mironov

In this work equations of average dynamics of accidentally-indignanted system of Volterra-Lotke are concluded and analysed on the basis of the method of Reynolds and the principle of maximum of entropia. This system describes behavior of a predator-prey model with accidental external noises. In general case models of such type are used in other problems, for example, in model of dynamics of appearance of clasters of chemical elements under the action of radiation. As result of averaging and application of the method of maximum entropia we receive five equations with five unknown quantities. Station point exists and the law of preservation of destiny entropia is carryed in this system. This law allows to analyze the global trajectories of system. Correlation inequality is introduced. It determined condition of approachibility of station point. The general properties of received system is investigated. The steadiness of model is analysed. It-s shown that unique station point of average system is not steady. However in system there is condition near by solutions of nonindignanted system. It-s condition with maximum entropia. It-s shown by direct calculations that condition with maximum entropia is condition steaded on Lyapunov. Also in this work approximate equations of average dynamics are concluded for small and great dispersions of fluctuations cases. It-s shown that at small dispersion averaged system is the Volterra-Lotke model without external noises. And at great dispersion system will pass to condition with maximum entropia but only owing to statistic reasons. Thus, the dynamics of such system essentially depends on quantity of dispersion of noise at system, namely on value of parameter . The choise of sign of coefficient of correlation at condition with great dispersion and with small entropia is determined by latent dynamics of nonobservable quantities U and V. Therefore average dynamics of system at such asymptotics bound gains characteristic of accidental springs. The condition with maximum entropia is steady at general case and is asymptotically steady. It confirms the general heuristic conception of usage of principle of maximum of entropia on practice.