Bifurcation analysis and control of improved traffic flow model considering the effect of strong winds.

In recent years, the problem of traffic congestion has become increasingly serious, and research on traffic system control has become a new hotspot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable support points can alleviate traffic congestion from a new perspective. This article improves the full speed differential model considering strong wind models from the perspective of bifurcation control to adjust traffic flow. This article theoretically proves the existence conditions of Hopf bifurcation and saddle node bifurcation in the model and finds the stability mutation point of the transportation system stability. A nonlinear system feedback controller was designed for unstable bifurcation points using Chebyshev polynomial approximation and random feedback control methods. Without changing the system equilibrium point, the advance, delay, and elimination of Hopf bifurcation were achieved, and the abrupt behavior of the transportation system was controlled, thereby alleviating traffic congestion. This article explains the changes in the stability of complex transportation systems from the perspective of bifurcation analysis, which can better capture the characteristics of traffic flow. By adjusting the control parameters in the feedback controller, the influence of boundary conditions on the stability of the transportation system is fully described, and the influence of unstable focal points and saddle points on the system is suppressed, thereby slowing down the traffic flow. In addition, unstable bifurcation points can be eliminated, and the Hopf bifurcation can be controlled to advance, delay, and disappear, thereby achieving control over the stable behavior of the transportation system. This helps alleviate traffic congestion and also helps describe actual traffic phenomena.

Hopf bifurcation control of macroscopic traffic flow model considering vehicle braking effect.

Traffic congestion not only has a great impact on people's travel, but also increases energy consumption and air pollution. The control analysis of the macroscopic traffic flow model considering the vehicle braking effect is particularly important, reflecting the impact on the actual traffic flow density wave, so as to better solve the actual traffic problems. In this paper, based on a speed difference optimization speed model, the micro-macro-variables are transformed into a high-order continuous traffic flow model. Then, a random function considering the physical correlation of random components is added to the high-order continuous traffic flow model to establish a random traffic flow model that can reflect the uncertain behavior of traffic flow acceleration or deceleration. Based on this stochastic traffic model, the existence of Hopf bifurcation and bifurcation control of the traffic flow system model considering stochastic characteristics are derived by using Hopf bifurcation theorem. By Chebyshev polynomial approximation method, the stochastic problem of the system is transformed into the bifurcation control problem of its equivalent deterministic system. A feedback controller is designed to delay the occurrence of Hopf bifurcation and control the amplitude of the limit cycle. Without changing the equilibrium point of the system, the complete elimination of Hopf bifurcation can be achieved by controlling the amplitude of the limit cycle. That is, the feedback controller is used to modify the bifurcation characteristics of the system, such as the bifurcation appearing at the equilibrium point in the control system moves forward, moves backward or disappears, so as to achieve the effect of preventing or alleviating traffic congestion.