Transient Dynamics in the Random Growth and Reset Model

Entropy

Zoltán Néda¹  Lehel Csillag¹  TamásS. Biró² 

[1] Department of Physics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania;Wigner Research Centre for Physics, 1121 Budapest, Hungary;

关键词: growth and reset process;    master equation;    stationary distribution;    transient dynamics;   

DOI  :  10.3390/e23030306

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown