The bifurcation phenomenon of traffic flow model involves complex dynamic characteristics and is rarely studied.Therefore, an optimal velocity model is proposed to study the effects of driver’s memory on driving behavior and fuel consumption.The complex traffic phenomenon is analyzed and predicted by nonlinear dynamics.We obtain Hopf (H) bifurcation, saddle-node (LP) bifurcation, cusp (CP) bifurcation and Bogdanov-Taken (BT) bifurcation by using two-parameter bifurcation and single-parameter bifurcation methods.Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density evolution to describe the dynamic phenomena of uniform flow, stable and unstable crowded flow and stop-and-go.The variation characteristics of energy consumption near bifurcation are simulated numerically.The results show that characteristic of fuel consumption can be found by considering the influence of bifurcation, which can also provide some theoretical guidelines for a rational control of energy consumption.