Bifurcation Analysis of the Full Velocity Difference Model

Bifurcation is investigated with the full velocity difference traffic model. Applying the Hopf theorem, an analytical Hopf bifurcation calculation is performed and the critical road length is determined for arbitrary numbers of vehicles. It is found that the Hopf bifurcation critical points locate on the boundary of the linear instability region. Crossing the boundary, the uniform traffic flow loses linear stability via Hopf bifurcation and the oscillations appear.

[1]  Jean-Philippe Bouchaud,et al.  Mutual attractions: physics and finance , 1999 .

[2]  Jiang Rui,et al.  A Realistic Cellular Automaton Model for Synchronized Traffic Flow , 2009 .

[3]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[4]  Cheng Shiduan,et al.  Chaotic Control of Network Traffic , 2009 .

[5]  T. Nagatani.  Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Huang Hai-Jun,et al.  Analysis of Density Wave in Two-Lane Traffic , 2007 .

[7]  Kerner,et al.  Experimental features and characteristics of traffic jams. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  R. E. Wilson,et al.  Bifurcations and multiple traffic jams in a car-following model with reaction-time delay , 2005 .

[9]  K. Nakanishi,et al.  Bifurcation phenomena in the optimal velocity model for traffic flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[11]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[12]  Dirk Helbing,et al.  GENERALIZED FORCE MODEL OF TRAFFIC DYNAMICS , 1998 .

[13]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[14]  G. Stépán,et al.  Subcritical Hopf bifurcations in a car-following model with reaction-time delay , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  S. Dai,et al.  Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  徐猛,et al.  Behaviours in a dynamical model of traffic assignment with elastic demand , 2007 .

[17]  R. E. Wilson,et al.  Global bifurcation investigation of an optimal velocity traffic model with driver reaction time. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Zi-you,et al.  Evolution of Traffic Flow with Scale-Free Topology , 2005 .

[19]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  B. Kerner.  THE PHYSICS OF TRAFFIC , 1999 .

[21]  G. B. Whitham,et al.  Exact solutions for a discrete system arising in traffic flow , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[22]  Ziyou Gao,et al.  Congestion in different topologies of traffic networks , 2006 .

[23]  R. Jiang,et al.  Full velocity difference model for a car-following theory. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  I. Gasser,et al.  Bifurcation analysis of a class of ‘car following’ traffic models , 2004 .

[25]  T. Nagatani.  The physics of traffic jams , 2002 .