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Bifurcation analysis of a new stochastic traffic flow model

  • WenHuan Ai EMAIL logo , RuiHong Tian , DaWei Liu und WenShan Duan
Veröffentlicht/Copyright: 13. Oktober 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 24 Heft 5

Abstract

The stochastic function describing the stochastic behavior of traffic flow in the process of acceleration or deceleration can better capture the stochastic characteristics of traffic flow. Based on this, we introduce the stochastic function into a high-order viscous continuous traffic flow model and propose a stochastic traffic flow model. Furthermore, we performed the bifurcation analysis of traffic flow system based on the model. Accordingly, the traffic flow problem is transformed into the stability analysis problem of the system, highlighting the unstable traffic characteristics such as congestion. The model can be used to study the nonlinear dynamic behavior of traffic flow. Based on this model, the existence of Hopf bifurcation and the saddle-node bifurcation is theoretically proved. And the type of the Hopf bifurcation is theoretically derived. The model can also be used to study the mutation behavior of system stability at bifurcation point. From the density space-time diagram of the system, we find that the system undergoes a stability mutation when it passes through the bifurcation point, which is consistent with the theoretical analysis results.

Keywords: bifurcation analysis; phase-plane analysis; stability analysis; stochastic traffic flow model
Corresponding author: WenHuan Ai, College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu, 730070, China, E-mail:

Funding source: “Qizhi” Personnel Training Support Project of Lanzhou Institute of Technology

Award Identifier / Grant number: 2018QZ-11

Funding source: Natural Science Foundation of Gansu Province of China

Award Identifier / Grant number: No. 20JR5RA533

Funding source: China Postdoctoral Science Foundation Funded Project

Award Identifier / Grant number: No.: 2018M633653XB

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: No. 61863032

Funding source: Gansu Province Educational Research ProjectÂ

Award Identifier / Grant number: No. 2021A-166

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors would like to thank the anonymous referees and the editor for their valuable opinions. This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61863032, 11965019) and the Natural Science Foundation of Gansu Province of China under the Grant No. 20JR5RA533 and the China Postdoctoral Science Foundation Funded Project (Project No: 2019M633653XB) and the “Qizhi” Personnel Training Support Project of Lanzhou Institute of Technology (2018QZ-11) and Gansu Province Educational Research Project (Grant No. 2021A-166).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-10-21
Accepted: 2022-09-18
Published Online: 2022-10-13

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Article
  3. Hybrid solitary wave solutions of the Camassa–Holm equation
  4. Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
  5. A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
  6. Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
  7. Numerical modeling of the dam-break flood over natural rivers on movable beds
  8. A class of piecewise fractional functional differential equations with impulsive
  9. Lie symmetry analysis for two-phase flow with mass transfer
  10. Asymptotic behavior for stochastic plate equations with memory in unbounded domains
  11. Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
  12. A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
  13. Ground state solutions of Schrödinger system with fractional p-Laplacian
  14. Bifurcation analysis of a new stochastic traffic flow model
  15. An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
  16. Hilfer fractional stochastic evolution equations on infinite interval
  17. Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
  18. Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
  19. Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
  20. Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
  21. Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
  22. Shehu transform on time-fractional Schrödinger equations – an analytical approach
  23. A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
  24. Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
https://doi.org/10.1515/ijnsns-2021-0399
Schlagwörter für diesen Artikel
bifurcation analysis; phase-plane analysis; stability analysis; stochastic traffic flow model

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Article
  3. Hybrid solitary wave solutions of the Camassa–Holm equation
  4. Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
  5. A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
  6. Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
  7. Numerical modeling of the dam-break flood over natural rivers on movable beds
  8. A class of piecewise fractional functional differential equations with impulsive
  9. Lie symmetry analysis for two-phase flow with mass transfer
  10. Asymptotic behavior for stochastic plate equations with memory in unbounded domains
  11. Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
  12. A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
  13. Ground state solutions of Schrödinger system with fractional p-Laplacian
  14. Bifurcation analysis of a new stochastic traffic flow model
  15. An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
  16. Hilfer fractional stochastic evolution equations on infinite interval
  17. Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
  18. Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
  19. Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
  20. Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
  21. Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
  22. Shehu transform on time-fractional Schrödinger equations – an analytical approach
  23. A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
  24. Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
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