Dynamical Memories based on Inter-module Hebbian Correspondences with the Chaotic Neural Network Modules

Hebbian reinforcement learning in a modular dynamic network

We present a multi-population dynamic neural network model with binary activation and a random interaction pattern. The weights parameters have been speci ed in order to distinguish excitatory populations from inhibitory populations. Under speci c parameters, we design functional modules composed of two populations, one of excitatory neurons, one of inhibitory neurons. Such modules are found to...

Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

Blowout bifurcation and On-off intermittency in Pulse Neural Networks with Multiplec Modules

To study the mechanism by which high-dimensional chaos emerges in neural systems, the synchronization of chaotic firings in class 1 pulse neural networks composed of excitatory and inhibitory ensembles was analyzed. In the system with two modules (i.e., two pulse neural networks), blowout bifurcation and on-off intermittency were observed when the inter-module connection strengths were reduced ...

Dynamical Systems on Hilbert C*-Modules

Chaotic pattern transitions in pulse neural networks

In models of associative memory composed of pulse neurons, chaotic pattern transitions where the pattern retrieved by the network changes chaotically were found. The network is composed of multiple modules of pulse neurons, and when the inter-module connection strength decreased, the stability of pattern retrieval changed from stable to chaotic. It was found that the mixed pattern of stored pat...