Title :
On Some Necessary and Sufficient Conditions for a Recurrent Neural Network Model With Time Delays to Generate Oscillations
Author :
Feng, Chunhua ; Plamondon, Réjean ; O´Reilly, Christian
Author_Institution :
Coll. of Math. Sci., Guangxi Normal Univ., Guilin, China
Abstract :
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.
Keywords :
Lyapunov methods; delays; oscillations; recurrent neural nets; Liapunov functional; fixed point theory; neural interconnections; oscillations generation; recurrent neural network model; time delays; unique equilibrium point; Associative memory; Biological system modeling; Councils; Delay effects; Delay systems; Neural networks; Propagation delay; Recurrent neural networks; Stability analysis; Sufficient conditions; Fixed point theory; necessary and sufficient conditions; oscillations; time delay recurrent neural network model; Animals; Biological Clocks; Central Nervous System; Computer Simulation; Feedback; Humans; Nerve Net; Neural Networks (Computer); Reaction Time; Time Factors;
Journal_Title :
Neural Networks, IEEE Transactions on
DOI :
10.1109/TNN.2010.2047512
