Passenger's fluctuation and chaos on ferryboats

We study the fluctuation of shipping passengers on a few ferryboats which shuttle between an origin and a destination repeatedly. We present the dynamical model for the ferryboats. The model is described in terms of nonlinear maps defined from the vectors T_i(n) and W_i(n), i=1, 2, …, N for N ferryboats where T_i(n) is the arrival time of ferryboat i at the origin on trip n and W_i(n) the number of passengers waiting at the origin on trip n. We clarify the fluctuations of shipping passengers and tour time for the ferry schedule. It is found that the dynamical transitions among the regular, periodic, and chaotic motions occur by varying the ferry's capacity F_max, headway T_min, and loading parameter ΓΠ. Even if the second ferryboat follows the leader (first ferryboat) keeping the constant headway, the passengers shipping on the second fluctuate highly when the parameters take specific values.