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
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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 -