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1·Positive maximum Lyapunov exponent was obtained from the signals, showing certain chaos features.

研究表明，肌电信号具有正的李雅谱诺夫指数，表现出一定的混沌特征。

2·First, the largest Lyapunov exponent of arc voltage waveform is calculated to confirm the chaotic behavior of arc furnace.

分析表明：该法用于直流电弧炉电气特性的建模研究，且进一步提高了预测的准确性。

3·Using the Lyapunov exponent, writers can simply show the chaotic behavior when a circuit oscillating in triangular waveform is off synchronization.

当一个生成三角波的回路同步失稳时，利用李亚普诺夫函数可以很容易证明系统实际上处于混沌态。

4·Based on conditional Lyapunov exponent, the impulsive synchronization form and interval of chaotic systems are studied, which breaks the traditional basic assumptions.

基于条件李亚普诺夫指数，对混沌系统的脉冲同步形式和同步范围进行了研究，突破了传统的基本假设。

5·Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section, Lyapunov exponent, and correlation dimension.

方法利用庞加莱截面、李雅普·诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。

6·The results show that both periodic and transitional chaotic sequences have positive maximum Lyapunov exponent, and the small data sets method is robust to the finite word length of the computer.

通过数值计算结果表明：有限字长混沌序列的周期态和过渡态都具有正的最大Lyapunov指数，且小数据量法对有限字长效应是鲁棒的。

7·When the coupled systems are chaotic, that is, the largest Lyapunov exponent is positive, the measure synchronization does not go with the phase synchronization, the phase locking changes random walk.

系统做混沌运动，测度同步时系统的相位移是随机行走的，没有测度同步点与相锁定点的重合。