Kink–antikink density wave of an extended car-following model in a cooperative driving system

A novel car following model considering average speed of preceding vehicles group

“…In this direction, scholars successively developed some extended multiple car following models based on OV model or FVD model. Some were extended by introducing multiple information of headway [20][21][22][23][24][25][26] or relative velocity [27][28][29], while others considered both factors at the same time [30][31][32]. Stability analysis in the aforementioned models all turn out that the stability of traffic flow is greatly improved.…”

Effect of the car-following combinations on the instability of heterogeneous traffic flow

“…Research on traffic instabilities has been conducted in traffic flow theory since 1950s (Herman et al 1959). Both linear and nonlinear stability analysis methods have been applied to study traffic instabilities using either microscopic models (Herman et al 1959;Wilson et al 2004;Treiber, Kesting, and Helbing 2005;Kesting and Treiber 2008;Yu, Shi, and Zhou 2008;Li et al 2009Li et al , 2011Tian, Sun, and Zhang 2011;Kesting 2011, 2013;Peng et al 2012;Tang et al 2012;Zheng et al 2012) or macroscopic models (Wilson et al 2004;Katiyar 2005, 2006;Zhang and Wong 2006;Tang, Huang, and Xu 2008;Helbing and Johansson 2009;Ngoduy and Tampere 2009;Tang et al 2011;Kesting 2011, 2013;Zhang, Wong, and Dai 2011;Ngoduy 2012aNgoduy , 2012bNgoduy , 2013aNgoduy , 2013bGupta and Dhiman 2014;Ngoduy 2014;Ngoduy and Wilson 2014). However, very little effort has been undertaken to perform such stability analysis in the context of heterogeneous traffic flow.…”

Bifurcation analysis of a speed gradient continuum traffic flow model

“…We obtain the Jacobian matrix of the system (10) at the equilibrium points (ρ i , 0) as (12) and the Jacobian characteristic equation as…”