粘弹性梁振动系统的稀有和隐藏吸引子及其演化特性研究OA

The global dynamics of multi-stable behavior in a nonlinear viscoelastic beam vibration system is studied from the perspective of rare and hidden attractors.The multi-stable attractor modes and existence regions of the system under the coupling of parameter plane and state plane are identified.The rare and hidden attractors and their causes of formation and disappearance in multi-stable states are revealed by combining the Runge-kutta,shooting and cell mapping methods.The results indicate that the viscoelastic beam vibration system presents many types of complex multi-stable behaviors,and some small changes in system parameters can cause rapid changes in the number and properties of multi-stable attractors.Saddle-node and period-doubling bifurcations are the main causes of generation and disappearance for rare attractors.Saddle-node,period-doubling and pitchfork bifurcations as well as merging crisis and boundary crisis may cause the emergence and disappearance of hidden attractors.There is no necessary connection between the hidden and rare properties of the attractor,both of which depend on the global dynamics of the system.