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Nomura Y, Saito S, Ishiwata R, et al. Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic. Phys Rev E. 2016;93(1):012215doi: 10.1103/PhysRevE.93.012215.
Nomura, Y., Saito, S., Ishiwata, R., & Sugiyama, Y. (2016). Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic. Physical review. E, 93(1), 012215. https://doi.org/10.1103/PhysRevE.93.012215
Nomura, Yasuyuki, et al. "Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic." Physical review. E vol. 93,1 (2016): 012215. doi: https://doi.org/10.1103/PhysRevE.93.012215
Nomura Y, Saito S, Ishiwata R, Sugiyama Y. Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic. Phys Rev E. 2016 Jan;93(1):012215. doi: 10.1103/PhysRevE.93.012215. Epub 2016 Jan 22. PMID: 26871081.
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Phys Rev E. 2016 Jan;93(1):012215. doi: 10.1103/PhysRevE.93.012215. Epub 2016 Jan 22.

Hopf bifurcation analysis for a dissipative system with asymmetric interaction: Analytical explanation of a specific property of highway traffic.

Physical review. E

Yasuyuki Nomura, Satoshi Saito, Ryosuke Ishiwata, Yuki Sugiyama

Affiliations

  1. Department of Electronics and Information Engineering, National Institute of Technology, Fukui College, Sabae 916-8507, Japan.
  2. Department of Information Engineering, Graduate School of Information Science, Nagoya University Nagoya 464-8601, Japan.
  3. Department of Complex Systems Science, Graduate School of Information Science, Nagoya University Nagoya 464-8601, Japan.

PMID: 26871081 DOI: 10.1103/PhysRevE.93.012215

Abstract

A dissipative system with asymmetric interaction, the optimal velocity model, shows a Hopf bifurcation concerned with the transition from a homogeneous motion to the formation of a moving cluster, such as the emergence of a traffic jam. We investigate the properties of Hopf bifurcation depending on the particle density, using the dynamical system for the traveling cluster solution of the continuum system derived from the original discrete system of particles. The Hopf bifurcation is revealed as a subcritical one, and the property explains well the specific phenomena in highway traffic: the metastability of jamming transition and the hysteresis effect in the relation of car density and flow rate.

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