Recurrence analysis of a Moore-Spiegel electronic circuit

Abstract

An electronic circuit that simulates theMoore-Spiegel equations [Moore and Spiegel, 1966] is presented. To compare the data measured from the circuit with the numerical solution to the equations, and assess the extent to which the circuit behaviour deviates from the model equations, parameter regimes are explored in each case. After going through a comparison of the two and performing a bifurcation analysis, we unravel the structure revealed by the circuit data.

In this study, recurrence plots [Eckmann, Kamphorst and Ruelle, 1987] are used to assess dynamical changes such as mode transitions and nonstationarity. Their diagnostic power is coupled with that of space time separation plots [Provenzale, Smith, Vio and Murante, 1992]. The quality of recurrence plots obtained from multi channel measurements is compared with that obtained by embedding a scalar signal into higher dimensions. The effect of nonstationarity on the time delay computed by the mutual information technique [Fraser and Swinney, 1986] is addressed.