1. Classification functions of chaotic pulse-coupled networks
Hidehiro Nakano and Toshimichi Saito
Electronics, Electrical and Computer Engineering Hosei University, Japan

2. Pulse-Coupled Network (PCN)
Introduction
Pulse-Coupled Network (PCN)
IFO: Integrate-and-Fire Oscillator
Relate to neural network
Various synchronous phenomena
[3] R.E.Mirollo et al. 1990
[4] E.Catsigeras et al. 1990
Engineering applications
Associate memory
Pulse-coupled network (PCN) is known as a kind of artificial neural network.
PCN consists of integrate-and-fire oscillators (IFOs).
This figure shows basic dynamics of the IFO.
V is a state of the IFO.
Applying input, the state increases like this.
If the state reaches this red threshold, the IFO outputs a spike signal like this, and the state is reset to this blue base instantaneously.
Repeating in this manner, the IFO outputs a spike-train.
In the PCN, each IFO is coupled by this spike-train.
Although the PCN is a simple coupled system, it exhibits various synchronous phenomena.
Some engineering applications of the PCNs have been proposed.
They include dynamical associative memories, image processing, and so on.
In this talk, we consider a PCN consisting of chaotic oscillators, and clarify what kinds of phenomena occur.
Based on obtained results, we consider applications of such a chaotic PCN.
[5] E.M.Izhikevich 1999
[6] G.Lee et al. 2002
Image processing
[8] S.R.Campbell et al. 1999
PCN of chaotic oscillators: phenomena ? applications ?

3. Chaos SYN (2-cells CPCN)
Next, we show typical experimental results.
Left figures show the 1st CSO’s attractor, time-domain waveform, and spike-train.
Right figures show the 2nd CSO’s.
This is the phase relationship between the 1st and 2nd CSOs.
As the 1st and 2nd CSOs have the almost same parameters, they exhibit in-phase chaos synchronization like this, and output synchronous spike-trains like these.

4. SYN Breakdown (2-cells CPCN)
As the parameters of the frequencies differ, the chaos synchronization changes into breakdown like this, and these CSOs output asynchronous spike-trains like these.

5. Grouping SYN (4-cells Ladder CPCN)

6. Simulation Results for Lattice CPCN
Oscillator Index

7. Simulation Results
Grouping
Group index

8. Image segmentation