Rotation Map with a Controlling Segment: Basic Analysis and Application to A/D Converters

This paper studies the rotation map with a controlling segment. As a parameter varies, the map exhibits superstable periodic orbits, chaos and rich bifurcation phenomena. The map is applicable to an A/D converter having efficient resolution characteristics. The converter can be realized as a circuit model based on a spiking neuron and the rate-coding. Presenting a test circuit, basic operation is confirmed experimentally.

[1]  Toshimichi Saito,et al.  Synchronization phenomena in pulse-coupled networks driven by spike-train inputs , 2004, IEEE Transactions on Neural Networks.

[2]  Toshimichi Saito,et al.  Analysis of Piecewise Constant Models of Current Mode Controlled DC-DC Converters , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[3]  Tracy Allen,et al.  On the arithmetic of phase locking: Coupled neurons as a lattice on R2 , 1983 .

[4]  T. Tsubone,et al.  Stabilizing and destabilizing control for a piecewise-linear circuit , 1998 .

[5]  Toshimichi Saito,et al.  Quantized Spiking Neuron With A/D Conversion Functions , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Avideh Zakhor,et al.  New properties of sigma-delta modulators with DC inputs , 1992, IEEE Trans. Commun..

[7]  Kazuyuki Aihara,et al.  Fisher information for spike-based population decoding. , 2006, Physical review letters.

[8]  R. Stoop,et al.  Renormalization Approach to Optimal Limiter Control in 1-D Chaotic Systems , 2002 .

[9]  T. Allen,et al.  Complicated, but rational, phase-locking responses of an ideal time-base oscillator , 1983 .

[10]  S. Doi.  A chaotic map with a flat segment can produce a noise-induced order , 1989 .

[11]  Toshimichi Saito,et al.  Rich Superstable Phenomena in a Piecewise Constant Nonautonomous Circuit with Impulsive Switching , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[12]  T. Saito,et al.  A Basic A/D Converter with Trapping Window , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[13]  L. O. Chua,et al.  The effect of integrator leak in Σ-Δ modulation , 1991 .

[14]  Robert M. Gray,et al.  Oversampled Sigma-Delta Modulation , 1987, IEEE Trans. Commun..

[15]  Nikolai F. Rulkov,et al.  Pseudo-chaotic time hopping for UWB impulse radio , 2001 .