A collection of N cells placed at the vertices of a 2d lattice, is considered. Each individual cell can contain no more than one particle. Every particle can emerge from an infinite reservoir of particles or get eliminated into it. At any given moment t, every cell is possible to exist in one of two distinct states A (unoccupied ) or B (occupied). If at time t a cell is in A, the probability of transitioning to B within the infinitesimal interval [t,t+Dt) equals wABDt. Conversely, if at time t it is in B, then the probability of transitioning back to state A equals wBADt.

In this work, the following topics are studied: 1) A master equation that describes the evolution of each cell is derived and the limiting behaviour of its solution is obtained. 2) A Lyapunov function that corresponds to the master equation is constructed.

It is demonstrated and confirmed experimentally that, regardless of its initial state, the system converges towards its equilibrium state. It is confirmed that the stationary state of the system is described by a Poisson distribution.

Papamichalis, K. (2024). Birth-Decay Process Model. Retrieved August 7, 2024, from http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html

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