Influences of nonideal characteristics of A-D converter on estimation of the Lyapunov exponent of one-dimensional discrete-time dynamical systems

The Lyapunov exponent is a means of quantitatively evaluating the orbit instability of a dynamical system. In calculating the Lyapunov exponent by measuring the time series from a dynamical system, it is necessary to input the time series data into a computer system using an A-D converter. However, since rounding errors or nonideal characteristics exist and external noise is contained in the A-D converter, the Lyapunov exponent estimated from the measured time series may differ from the true value. In this paper, assuming the offset error, gain error, integral nonlinear error, differential nonlinear error as errors due to the nonideal characteristics of the A-D converter, the effects of these nonideal characteristics on the estimation of the Lyapunov exponent of a one-dimensional discrete-time dynamical system are investigated.