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With the help of discontinuous mapping and tail mapping, the maximum Lyapunov exponent of the system with the above three structures was constructed using Khasminskii transform. For the shape memory alloy beam model with unilateral constraints, the corresponding Lyapunov exponent sequences were analyzed and the bifurcation and chaotic motions of the system were discussed. The results show that the validity of the maximum Lyapunov exponent algorithm is verified by combining the time history diagram and phase diagram. [ABSTRACT FROM AUTHOR]

Given the discontinuous structure of vibro-impact system. Newton iteration was used to establish an effective numerical integration strategy. and this numerical integration strategy was applied to the cell mapping algorithm. The effectiveness of this method was verified by an application example of a typical duffing vibro-impact system. and the global coexistence attractor and global catastrophe of the system were further discussed. The research shows that Newton iterative integration method is suitable for vibro-impact system, and the study of periodic motion and chaotic motion of the system is not only effective, but also efficient. The algorithm can quickly lo- cate the collision time and improve the calculation speed. With the change of parameters. there are abundant catastrophe phenomena in the vibro-impact system. including the rout from period directly to chaos. the crisis of multi-periodic solution and chaotic solution. [ABSTRACT FROM AUTHOR]