Master-Slave Coupled Piecewise Constant Spiking Oscillators

This paper presents pulse-coupled piecewise constant spiking oscillators (PWCSOs) consisting of two PWCSOs and a coupling method is master-slave coupling. The slave PWCSO exhibits chaos because of chaotic response of the master one. However, if the parameter varies, the slave PWCSO can exhibit the phenomena as a periodicity in the phase plane. We focus on such phenomena and corresponding bifurcation. Using the 2-D return map, we clarify its mechanism.

[1]  J. Rinzel,et al.  INTEGRATE-AND-FIRE MODELS OF NERVE MEMBRANE RESPONSE TO OSCILLATORY INPUT. , 1981 .

[2]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[3]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[4]  T. Saito,et al.  Dependent switched capacitor chaos generator and its synchronization , 1997 .

[5]  DeLiang Wang,et al.  Synchrony and Desynchrony in Integrate-and-Fire Oscillators , 1999, Neural Computation.

[6]  Eugene M. Izhikevich,et al.  Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory , 1999, IEEE Trans. Neural Networks.

[7]  Eugene M. Izhikevich,et al.  Resonate-and-fire neurons , 2001, Neural Networks.

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

[9]  Nabil H. Farhat,et al.  The Bifurcating Neuron Network 2: an analog associative memory , 2002, Neural Networks.

[10]  Toshimichi Saito,et al.  Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators , 2004, IEEE Transactions on Neural Networks.

[11]  Toshimichi Saito,et al.  Rich dynamics of pulse-coupled spiking neurons with a triangular base signal , 2005, Neural Networks.

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

[13]  Toshimichi Saito,et al.  A Simple Chaotic Spiking Oscillator Having Piecewise Constant Characteristics , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

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