Abstract
In this paper, we have studied the power spectra of the entire particle occupancy in the totally asymmetric exclusion processes on lattices with a junction, at which two lanes I and II merge into lane III. We have performed the investigations, utilizing both Monte Carlo simulations and theoretical analysis based on linearized Langevin equations. The effect of lane length, particle entry rates at lanes I and II, and particle exit rate at lane III have been discussed. The transition from damped periodic oscillation to irregular oscillation as well as disappearance of oscillation has been observed. In particular, when lanes I, II, III are simultaneously in low density (LD) state or high density (HD) state, and the length [Formula: see text] of lane I is not remarkably different from the length [Formula: see text] of lane II, the damped periodic oscillations could be observed and the minima of the power spectra could be calculated via weighted average. However, when [Formula: see text] is notably different from [Formula: see text], the oscillation becomes irregular.
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