Hopf bifurcation analysis and control of the continuum model considering the new energy vehicles effect

Wenhuan Ai (), Dongliang Fang (), Jianli Fu () and Dawei Liu ()
Additional contact information
Wenhuan Ai: Northwest Normal University
Dongliang Fang: Northwest Normal University
Jianli Fu: Northwest Normal University
Dawei Liu: Lanzhou Institute of Technology

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 1, 1-18

Abstract: Abstract The research of traffic congestion control has been developed rapidly in recent years. Researching the bifurcation characteristics of traffic flow and designing control schemes for unstable bifurcation points can provide some new methods for relieving the traffic congestion. In this paper, we study the bifurcation characteristics and nonlinear control of traffic flow based on the continuum model considering the new energy vehicles effect. First, a macroscopic traffic flow model considering the number of new energy vehicles and their range is proposed. Then, we transform it into a traffic flow stability model suitable for branching analysis using the traveling wave transformation. Therefore, we can transform the traffic flow problem into the stability analysis problem of systems and reflect unstable traffic characteristics such as congestion. Based on the stability model, the existence conditions of the Hopf bifurcation are proved and some bifurcation points of the traffic system are found. Second, we study the congestion and stability abrupt change behaviors near the equilibrium point and branching point to seek for the formation mechanism of traffic congestion. Finally, for the unstable bifurcation point, the control scheme is designed by Chebyshev polynomial approximation, stochastic feedback control, and other methods to delay or disappear the unstable bifurcation point and alleviate traffic congestion. It has important theoretical significance and application value. Graphical abstract

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-023-00638-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:97:y:2024:i:1:d:10.1140_epjb_s10051-023-00638-4

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-023-00638-4

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().