Does negative Lyapunov Exponent means non-chaotic gait signal?

[Saikat Chakraborty]

I am examining the stability of a normal gait through a kinematic parameter (Displacement) analysis.I am getting negative Lyapunov exponent in Z-direction (vertical) but positive in other directions for the same body position (calcaneus) data.For displacement parameter, the vertical direction is considered in the literature.I am using treadmill data which is captured by Vicon camera.

Does negative Lyapunov exponent in vertical direction means gait signal is non-chaotic? If it is, then what about other direction?

[Jenna Yentes]

Re: Does negative Lyapunov Exponent means non-chaotic gait signal?

Hi Saikat,

You should remember that LyE does not measure stability in the sense you are describing it above. It is a measure of the rate of divergence of a trajectory and its units are bits/second (unless normalized to stride or something and then bits/stride). A negative LyE indicates that the trajectory is converging on itself. Converging to a fixed point orbit. A positive LyE indicates that the trajectory is expanding. Chaotic and random systems may have a positive LyE; thus why you need to do surrogation to determine the nature of the signal if it is a positive LyE. A LyE = 0 indicates a mathematically stable orbit (neither converging or diverging).

Also keep in mind, you are probably calculating the largest LyE. Mathematically, there is a LyE for each dimension of the trajectory. However, the algorithm you select may only give you the largest (or first). Hope this helps.

Jenna