TY - JOUR

T1 - Periodic solutions of a non-linear traffic model

AU - Safonov, L. A.

AU - Tomer, E.

AU - Strygin, V. V.

AU - Havlin, S.

PY - 2000/9/15

Y1 - 2000/9/15

N2 - A car-following model of single-lane traffic is studied. Traffic flow is modeled by a system of Newton-type ordinary differential equations. Different solutions (equilibria and limit cycles) of this system correspond to different phases of traffic. Limit cycles appear as results of Hopf bifurcations (with density as a parameter) and are found analytically in small neighborhoods of bifurcation points. A study of the development of limit cycles with an aid of numerical methods is performed. The experimental finding of the presence of a two-dimensional region in the density-flux plane is explained by the finding that each of the cycles has its own branch of the fundamental diagram.

AB - A car-following model of single-lane traffic is studied. Traffic flow is modeled by a system of Newton-type ordinary differential equations. Different solutions (equilibria and limit cycles) of this system correspond to different phases of traffic. Limit cycles appear as results of Hopf bifurcations (with density as a parameter) and are found analytically in small neighborhoods of bifurcation points. A study of the development of limit cycles with an aid of numerical methods is performed. The experimental finding of the presence of a two-dimensional region in the density-flux plane is explained by the finding that each of the cycles has its own branch of the fundamental diagram.

UR - http://www.scopus.com/inward/record.url?scp=0034275481&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(00)00278-8

DO - 10.1016/S0378-4371(00)00278-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.conferencearticle???

AN - SCOPUS:0034275481

SN - 0378-4371

VL - 285

SP - 147

EP - 155

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

T2 - Proceedings of the 36th Karpacz Winter School in the Theoretical Physics

Y2 - 11 February 2000 through 19 February 2000

ER -