中文摘要：

文章主要研究了一类三次Kukles系统和一个具体的非线性动力学模型的Lyapunov量复算法.借助Maple数学软件应用Lyapunov量复算法在一定程序下计算出三次Kukles系统的Lyapunov量,并证明出原点的最高阶细焦点阶数为3,也给出在两组不同数据下原点成为三阶细焦点的稳定性;又结合特征值和Lyapunov量复算法研究一个形状记忆合金薄板确定的具体的非线性动力学模型的平衡点成为中心的判定问题.重点讨论了通过把该非线性动力学模型转化为文中的基本复形式,由Lyapunov量复算法得出原点成为中心的充分条件.

英文摘要：

The complex algorithm of Lyapunov values for one cubic kukles system and one concrete nonlinear dynamic model was studied.The Lyapunov values of this cubic Kukles system were computed by applying the complex algorithm of Lyapunov values with Maple software under certain program.It was also proved that the highest order of fine focus was 3 and the stability of origin being a third-order fine focus were given under two different data.Moreover,the problem of deterining equilibrium point being center for nonlinear dynamic model determined was analyzed by shape memory alloy plane by combining eigenvalue with the complex algorithm of Lyapunov values.The sufficient conditions of origin being center were presented by the complex algorithm of Lyapunov values through converting this nonlinear dynamic modle into the basic complex form in paper.