In this repository you can find an implementation of the scaled voter model. In this particular implementation the transition rates are power-law functions of time. With this modification voter model behaves as if driven by the scaled Brownian motion, instead of the usual Brownian motion. From the perspective of anomalous diffusion (temporal evolution of the first two moments) and first passage times scaled Brownian motion is equivalent to the fractional Brownian motion.
The difference from most implementation of the voter model, this technically differs in two regards:
- Modified next reaction method is used (instead of the usual rejection-based methods or Gillespie method).
- Simulation scales (number of agents is increased) when most agents occupy the same state (X/N approaches either 0 or 1).
Shell scripts contained in this repository were used to obtain data used to produce figures from [1]. In the said paper you can find more details as well as analytical approximations for the simulation results.
Note: Model itself was implemented in C, to properly run it you will
have first to make (compile) it. Makefile is in the crun directory.
- R. Kazakevičius, A. Kononovicius. Anomalous diffusion and long-range memory in the scaled voter model. Physical Review E 107: 024106 (2023). doi: 10.1103/PhysRevE.107.024106. arXiv:2301.08088 [cond-mat.stat-mech].