Threshold for horseshoe chaos in fractional-order hysteretic nonlinear suspension system of vehicle

The chaotic behavior of a nonlinear vehicle suspension system with a fractional-order derivative is considered. A hysteretic nonlinear model of vehicle suspension with a fractional-order derivative term is established and the analytically necessary condition for heterotopic chaos is derived based on the Melnikov method. The largest Lyapunov exponents are compared. Then, the necessary condition is numerically verified by various simulation factors. The possibility of chaotic motion in vehicles should be higher for larger amplitude of road excitation. It is found that the coefficient and order of the fractional differential term, the stiffness coefficient, and the damping coefficient of the system all affect the necessary condition, and analysis on the effects of these parameters is presented individually. It has been shown that the larger the coefficient of the fractional differential term, or the stiffness and damping coefficients of the system, the lower the possibility of chaos in the system. Meanwhile, without considering the fractional order, the integer order suspension model obviously reduces the actual area where chaos may occur, so designing suspensions according to the fractional order model can avoid chaos more accurately than the integer order model.