Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contribu...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2021-03, Vol.23 (3), p.306
Main Authors: Biró, Tamás S, Csillag, Lehel, Néda, Zoltán
Format: Article
Language:English
Subjects:
Evolution
growth and reset process
master equation
Partial differential equations
stationary distribution
transient dynamics
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Summary:A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23030306