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arXiv · 1201.2141

Asymptotic behaviour in the time synchronization model

Vadim Malyshev·Anatoly Manita
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Abstract

There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}α_{ij}$. We discuss in details the initial desynchronization of this particle system, namely, we are interested in behaviour of the process when the total number of particles $N_1+N_2$ tends to infinity, the ratio $N_1/N_2$ is constant and the time $t>0$ is fixed.

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Vadim Malyshev, Anatoly Manita. 2012-01-10. Asymptotic behaviour in the time synchronization model. https://arxiv.org/abs/1201.2141

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