Newton iterative integration method and global dynamics of vibro-impact system

Abstract

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 locate 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.

Keywords

• vibro-impact system
• newton iterative integration method
• cell mapping method
• global structure