On Some Necessary and Sufficient Conditions for a Recurrent Neural Network Model With Time Delays to Generate Oscillations

• Published in: IEEE transaction on neural networks and learning systems 2010-08, Vol.21 (8), p.1197-1205
• Main Authors: Chunhua Feng, Plamondon, R, O'Reilly, C
• Format: Article
• Language: English
• Subjects: Animals; Applied sciences; Artificial intelligence; Associative memory; Biological Clocks - physiology; Biological system modeling; Central Nervous System - physiology; Computer science; control theory; systems; Computer simulation; Computer Simulation - standards; Connectionism. Neural networks; Councils; Criteria; Delay effects; Delay systems; Exact sciences and technology; Feedback; Fixed point theory; Humans; Mathematical models; necessary and sufficient conditions; Nerve Net - physiology; Networks; Neural networks; Neural Networks (Computer); Oscillations; Propagation delay; Reaction Time - physiology; Recurrent neural networks; Stability analysis; Sufficient conditions; Time delay; time delay recurrent neural network model; Time Factors
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2010.2047512

In this paper, the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated. By using the fixed point theory and Liapunov functional, we prove that a recurrent neural network might have a unique equilibrium point which is unstable. This particular type of instability, combined with the boundedness of the solutions of the system, will force the network to generate a permanent oscillation. Some necessary and sufficient conditions for these oscillations are obtained. Simple and practical criteria for fixing the range of parameters in this network are also derived. Typical simulation examples are presented.