Abstract
Lyapunov exponent is an indicator which expresses the degree of sensitivity to initial condition of
dynamical systems; Lyapunov exponent expresses the level of chaos. Rosenstein et al.1） developed the
way to calculate Lyapunov exponents from an experimental non-linear time series which is robust to
noise. This method needs the time series to be stationary, but, in many cases, it is difficult to get
stationary time series. For example, response of neuron,2） human brain signals3） are said to be chaotic,
but chaos levels of these experimental time series are not stationary4）; characteristics of time series
changes from time to time depending on conditions. Then, we developed Moving Maximum Lyapunov
Exponents (MMLE) based on Rosenstein’s way. MMLE shows the changing Lyapunov exponents of
time series, therefore we can know the chaos level at each time and changes of dynamics in time series.
We suggest MMLE will be new way of non-linear time series analysis.
