Multifractal chaotic attractors in a system of delaydifferential equations modeling road traffic
Abstract
We study a system of delaydifferential equations modeling singlelane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the RuelleTakensNewhouse scenario (limit cyclestwotorithreetorichaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum.
 Publication:

Chaos
 Pub Date:
 December 2002
 DOI:
 10.1063/1.1507903
 Bibcode:
 2002Chaos..12.1006S
 Keywords:

 45.70.Vn;
 05.45.a;
 02.30.Oz;
 02.30.Hq;
 02.10.Ud;
 Granular models of complex systems;
 traffic flow;
 Nonlinear dynamics and chaos;
 Bifurcation theory;
 Ordinary differential equations;
 Linear algebra