A ternary logic model for recurrent neuromime networks with delay

In contrast to popular recurrent artificial neural network (RANN) models, biological neural networks have unsymmetric structures and incorporate significant delays as a result of axonal propagation. Consequently, biologically inspired neural network models are more accurately described by nonlinear...

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Bibliographic Details
Published in:Biological cybernetics 1995-07, Vol.73 (2), p.177-188
Main Authors: Hangartner, R D, Cull, P
Format: Article
Language:English
Subjects:
Animals
Cybernetics
Electrophysiology
Logistic Models
Mathematics
Models, Neurological
Mollusca - physiology
Nerve Net - physiology
Synapses - physiology
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Summary:In contrast to popular recurrent artificial neural network (RANN) models, biological neural networks have unsymmetric structures and incorporate significant delays as a result of axonal propagation. Consequently, biologically inspired neural network models are more accurately described by nonlinear differential-delay equations rather than nonlinear ordinary differential equations (ODEs), and the standard techniques for studying the dynamics of RANNs are wholly inadequate for these models. This paper develops a ternary-logic based method for analyzing these networks. Key to the technique is the realization that a nonzero delay produces a bounded stability region. This result significantly simplifies the construction of sufficient conditions for characterizing the network equilibria. If the network gain is large enough, each equilibrium can be classified as either asymptotically stable or unstable. To illustrate the analysis technique, the swim central pattern generator (CPG) of the sea slug Tritonia diomedea is examined. For wide range of reasonable parameter values, the ternary analysis shows that none of the network equilibria are stable, and thus the network must oscillate. The results show that complex synaptic dynamics are not necessary for pattern generation.
ISSN:0340-1200
1432-0770
DOI:10.1007/BF00204056