Bifurcations and multiple traffic jams in a car-following model with reaction-time delay

DOI10.1016/j.physd.2005.09.004zbMath1097.90015OpenAlexW2114834408MaRDI QIDQ2507967

Gábor Orosz, R. Eddie Wilson, Bernd Krauskopf

Publication date: 5 October 2006

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://research-information.bristol.ac.uk/en/publications/bifurcations-and-multiple-traffic-jams-in-a-carfollowing-model-with-reaction-time-delay(77d16a7d-893b-4f16-ae49-f13fdadd581b).html

zbMATH Keywords

periodic solutionstraffic modellingfront dynamicsfloquet multiplierstraffic patternsreaction-time delay

Mathematics Subject Classification ID

Automated systems (robots, etc.) in control theory (93C85) Traffic problems in operations research (90B20) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18)

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Uses Software

• AUTO
• DDE-BIFTOOL

Cites Work

• Unnamed Item
• One-dimensional unstable eigenfunction and manifold computations in delay differential equations
• Introduction to functional differential equations
• Dynamics in infinite dimensions. Appendix by Krzysztof P. Rybakowski.
• Modifications of the optimal velocity traffic model to include delay due to driver reaction time
• Bifurcation analysis of a class of `car following' traffic models
• Delay equations. Functional-, complex-, and nonlinear analysis
• Invariant manifolds for metastable patterns in u_t = ε²u_xx—f(u)
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Updated semi‐discretization method for periodic delay‐differential equations with discrete delay
• A NEWTON–PICARD COLLOCATION METHOD FOR COMPUTING PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS
• Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

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