Basic Bifurcation of Artificial Spiking Neurons with Triangular Base Signal

This paper studies a spiking neuron circuit with triangular base signal. The circuit can output rich spike-trains and the dynamics can be analyzed using a one-dimensional piecewise linear map. This system exhibits period doubling bifurcation, tangent bifurcation, super-stable periodic orbit bifurcation and so on. These phenomena can be characterized based on the inter-spike intervals. Using the maps, we can analyze the phenomena precisely. By presenting a simple test circuit, typical phenomena are confirmed experimentally.

[1]  Geehyuk Lee,et al.  The bifurcating neuron network 3 , 2005 .

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

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

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

[5]  Leon Glass,et al.  Bistability, period doubling bifurcations and chaos in a periodically forced oscillator , 1982 .

[6]  J J Hopfield,et al.  Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Hiroyuki Torikai,et al.  Synchronization via multiplex pulse trains , 1999 .

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

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

[10]  Hiroshi Kawakami,et al.  Connecting border collision with saddle-node bifurcation in switched dynamical systems , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[12]  Nikolai F. Rulkov,et al.  Chaotic pulse position modulation: a robust method of communicating with chaos , 2000, IEEE Communications Letters.

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

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