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The extinction probability in systems randomly varying in time
Imre P azsit,M.M.R. Williams,L en ard P al 한국원자력학회 2017 Nuclear Engineering and Technology Vol.49 No.6
The extinction probability of a branching process (a neutron chain in a multiplying medium) is calculatedfor a system randomly varying in time. The evolution of the first two moments of such a process wascalculated previously by the authors in a system randomly shifting between two states of differentmultiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than thatof the moments, and it can only be achieved by pure numerical methods. The numerical results indicatethat for systems fluctuating between two subcritical or two supercritical states, the extinction probabilitybehaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is acrucial and unexpected deviation from the predicted behaviour. The results bear some significance notonly for neutron chains in a multiplying medium, but also for the evolution of biological populations in atime-varying environment.
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