Codimension-two bifurcation analysis and chaos synchronization of a quarter-car vehicle model

Abstract

In this study, codimension-two bifurcation analysis was used in conjunction with a novel control method to mediate chaos in a semi-active suspension system based on a quarter-car model with excitation introduced by the road surface profile. The results of bifurcation analysis indicate that the hysteretic nonlinear characteristics of the damping forces produce codimension-two bifurcation, resulting in homoclinic orbits and pitchfork bifurcation. We also characterized the complex dynamics of vehicle suspension systems using a bifurcation diagram, phase portraits, Poincaré maps, and frequency spectra. Furthermore, the largest Lyapunov exponent was used to identify the onset of chaotic motion and to verify the results of bifurcation analysis. We also developed a continuous feedback control method based on synchronization characteristics to eliminate chaotic oscillations. Finally, we conducted analysis on the robustness of parametric perturbation in suspension systems with synchronization control using Lyapunov stability theory and numerical simulations.