FRACTAL BASIN BOUNDARIES AND CHAOTIC MOTIONS IN SPRING-PENDULUM SYSTEM

摘要

This study investigates chaotic response in the spring-pendulum system. In this system beside of strange attractors, multiple regular attractors may coexist for some values of system parameters, where it is important to study the global behavior of the system using the basin boundaries of the attractors. Multiple scales method is used to distinguish the regions of stable and unstable attractors. In unstable regions, bifurcation diagram and poincare maps are used to study the existence of quasi-periodic and chaotic attractors. Results show that the jumping phenomena may occur when multiple regular attractors exist and for this case fractal basins of attraction are developed using numerical simulations.