关键词: 龙格-库塔法, 混沌, 分岔, 相图, Poincare映像

Abstract: The model of forced and damped transverse oscillation of a symmetric double-spring oscillator is designed and its dynamical equation is proposed. By using the method of linear stability analysis, the stability of the system is discussed in the neighborhood of the equilibrium point. The character of the solution can be obtained by numerical simulation and other analysis methods. Time-series diagram, phase diagram and bifurcation diagram for the oscillation of this system are plotted. These results show that there are various kinds of dynamical phenomena. Theoretical analysis is in agreement with numerical simulation.

Key words: Runge-Kutta method, chaos, bifurcation, phase diagram, Poincare mapping diagram