Nonlinear dynamics of traffic flow stability: A review from car-following to mixed-autonomy

Traffic flow stability is fundamentally a nonlinear dynamic phenomenon, where the amplification of small disturbances into stop-and-go waves directly determines road efficiency, safety, and sustainability. This paper provides a systematic review of traffic flow stability research through the lens of nonlinear dynamics, based on a curated dataset of more than 150 Scopus documents. We begin with a bibliometric analysis mapping publication trends, influential authors, and thematic clusters. The review classifies car-following models and formally defines local, asymptotic, and string stability. Principal analytical methods, linear stability analysis, nonlinear perturbation methods, control-theoretic approaches, and simulation techniques are explained, emphasizing their roots in nonlinear science. We systematically examine homogeneous traffic stability, highlighting the roles of driver characteristics, time delays, and road geometry in shaping nonlinear wave dynamics. The major focus is mixed traffic, analysing how the penetration rate of connected automated vehicles, spatial distribution, platooning, communication imperfections, and human factors collectively influence the emergence and suppression of traffic waves. Critical research gaps are identified and future directions proposed, providing a comprehensive reference for researchers working at the intersection of nonlinear dynamics and next-generation transportation systems.