Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS
Volume 20, Issue 5, Pages 794-804Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2009.2013341
Keywords
Cellular nonlinear networks (CNNs); complete stability; counterclockwise (ccw) input-output (I-O) dynamics; Fitzhugh-Nagumo circuit; Hopfield CNN; passivity theory
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Funding
- Institut National de Recherche en Informatique et en Automatique (INRIA) de Rocquencourt
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The notion of counterclockwise (ccw) input-output (I-O) dynamics, introduced by Angeli (2(106) to deal with questions of multistability in interconnected dynamical systems, is applied and further developed in order to analyze convergence and stability of neural networks. By pursuing a modular approach, we interpret a cellular nonlinear network (CNN) as a positive feedback of a parallel block of single-input-single-output (SISO) dynamical systems, the neurons, and a static multiple-input-multiple-output (MIMO) system that couples them (typically the so-called interconnection matrix). The analysis extends previously known results by enlarging the class of allowed neural dynamics to higher order neurons.
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