A strategy for solving the static bifurcation points of the 5DOF vehicle nonlinear system is proposed to research the stability region of the system. The bifurcation characteristics of the system is changed by the coupling of the steering and the engine braking torques under the high-speed emergency steering conditions, and the corresponding vehicle stability region must be redefined. The stability region of the vehicle which is influenced by the engine braking torque is determined with the static bifurcation theory, and the equilibrium points of the 5DOF vehicle system are solved with the phase space method and the random weight particle swarm optimization (RWPSO) algorithm. The vehicle stability is verified with different initial longitudinal speeds and different steering angles, and the simulation results validate the effectiveness of the stability region under the critical driving conditions. The study is conducive to the development of the active safety control systems and the application of nonlinear system dynamics in the automotive field. Furthermore, it provides the theoretical support for the application of the vehicle-handling stability.

提出了一种求解5自由度车辆非线性系统静态分叉点的策略，以研究系统的稳定区域。在高速紧急转向条件下，转向和发动机制动扭矩的耦合会改变系统的分叉特性，因此必须重新定义相应的车辆稳定区域。利用静态分叉理论确定了受发动机制动扭矩影响的车辆稳定区域，并通过相空间法和随机权重粒子群算法（RWPSO）求解了5DOF车辆系统的平衡点。通过不同的初始纵向速度和不同的转向角验证了车辆的稳定性，仿真结果验证了关键驾驶条件下稳定区域的有效性。该研究有利于主动安全控制系统的开发以及非线性系统动力学在汽车领域的应用。此外，它为车辆操纵稳定性的应用提供了理论支持。