EMPLOYMENT OF AVERAGED Q-MATRICES IN ECOLOGY AND BIOLOGY WHEN DIAGNOSING
AND FORECASTING LONG-LIFE SYSTEMS WITH A FINITE NUMBER OF STATES

Ryzhakov Viktor Vasil'evich, Doctor of engineering sciences, professor, head of sub-department of technical quality management, Honoured Scientist of the Russian Federation, Penza State Technological Academy
(Penza, 1a Baidukova passage), rvv@pgta.ru
Ryzhakov Mikhail Viktorovich, Senior lecturer, sub-department of applied mechanics, head of laboratory of modern nanotechnologies and ecology studies, Moscow Institute of Physics and Technology (State University)
(Moscow Region, Dolgoprydny, 9 Institutsky lane), mryzhakov@applmech.mipt.ru

519.21.248+57+574

The article contains analytical guidelines of diagnosing (forecasting) long-life systems with the use of average Q-matrices. Provided are details of methodological peculiarities of averaging elements of Q-matrices. The article offers the algorithm synthesized with their use as based on the limit theorem for numerical homogeneous Markov chains (on majorant convergence) allowing of diagnosing and forecasting system conditions according to stability parameter. All analytical results are illustrated by numerical experiments. Their results prove sufficient response of the offered algorithm to the given data variations.

diagnosing, forecasting, probability, system, Q-matrix, Markov chains, ecology, biology.

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