This document describes the epl2 document class, used to typeset papers for EPL, the journal jointly published by Societ`a Italiana di Fisica, Italy, EDP Sciences, France, IOP Publishing, UK, under the scientific control of the European Physical Society.

In this paper, coupled-phase oscillator chains with localized three-body interactions are studied. Systems have rich patterns such as chimera and twisted states. The coupled-phase oscillator chains have long-range two-body interactions and short-range three-body interactions, which respectively play the role of long-range inhibition of short-range activation, just like inhibitors and activators in traditional reaction-diffusion systems. The role of three -body interaction in the system is studied through the Turing pattern diagram and the critical point of Turing instability is obtained. When Turing instability occurs, system approaches to twisted states and chimera states. The study indicates that long-range inhibition and short-range activation give an explanation for the formation of such coherent-incoherent modes such as chimera states, and that three-body interactions are good candidates as activators of the system. Our study can be applied to many-body interacting systems.
A lattice hydrodynamic traffic model considering the average optimal flow of multiple grids downstream as a feedback control is proposed. The energy dissipation and fuel consumption are investigated under the feedback control based on the lattice hydrodynamic traffic model. Through linear stability analysis, the stability condition of the model is obtained. The mKdV equation and its kink-antikink density wave solution are derived by using the reduced perturbation method of nonlinear analysis. The variation trends of density wave, energy dissipation, and fuel consumption under traffic control are studied by numerical simulations. The research shows that exerting the feedback control can effectively suppress traffic congestion and improve the stability of traffic system. Meanwhile, it can also reduce the energy dissipation and fuel consumption of traffic system.
In this paper, a lattice hydrodynamic model of four-way pedestrian traffic considering turning capacity is proposed. The stability conditions are obtained by stability analysis. The mKdV equation is derived using the reductive perturbation method of nonlinear analysis, and the corresponding density wave solutions are obtained. The results of theoretical analysis are verified by detailed numerical simulation of the spatial-temporal patterns of the density of pedestrian flow evolution under different initial conditions and the density profile at different moments. The results show that the balanced distribution of pedestrian flow along the horizontal and vertical passages can promote the stability of pedestrian traffic, and pedestrians turning at the intersections can stimulate traffic jams.
In this paper, in order to study the dynamic behavior of the three-body interaction, the generalized Kuramoto model with bimodal frequency distribution under the joint interaction of two-body and three-body is proposed. The comparative numerical results of the phase synchronization paths of the three-body interaction under different coupling strengths show that the three-body interaction can transform the continuous transition process into the first-order transition process. Interestingly, the change from continuous to discontinuous transition due to the variation of the coupling strength of the three-body interaction is similar to the shape of the bimodal distribution of the natural frequency. The critical coupling strength of the two-body interaction of synchronous transition is derived from the Ott–Antonsen–Ansatz method. The numerical results are consistent with the theoretical ones. The findings help our understanding of the transformation process from being continuous to discontinuous.
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