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中文摘要：
研究了一类具有对称性的三次方一维离散系统的非线性动力学行为．发现随着系统控制参数的变化，这一类C^2类非单峰的映射有着丰富的动力学行为．在一定的参数区域内，系统历经倍周期分岔、鞍结分岔、对称性破缺分岔等形式通向混沌．利用分岔图、Floquet乘子、Lyapunov指数等对系统的周期遍历和混沌现象进行了详细的分析，并计算了系统发生对称性破缺分岔点和对称性恢复点．
英文摘要：
In this paper, the nonlinear dynamics analysis to a cubic one dimensional symmetry discrete system is studied, There is plenty of nonlinear dynamics behavior in this-type of non-single peak map when changing the control parameter. The system could undergo the period-doubling bifurcation, saddle-note bifurcation, symmetry-breaking bifurcation and so forth tO chaos, as the control parameter was set on some certain intervals. The periodic motion and the chaotic phenomena of the system was analyzed in details by the bifurcation diagrams, Floquet multipliers, Lyapunov exponent, etc, and both symmetry-breaking bifurcation point and symmetry-recovering bifurcation point were calculated.
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