Stability Analysis of a Class of Three-Neuron Delayed Cellular Neural Network
Poulami D. Gupta, N. C. Majee and A. B. Roy
DOI : 10.3844/ojbsci.2010.36.43
OnLine Journal of Biological Sciences
Volume 10, Issue 1
Problem statement: In this study linear stability of a class of three neuron cellular network with transmission delay had been studied. Approach: The model for the problem was first presented. The problem is then formulated analytically and numerical simulations pertaining to the model are carried out. Results: A necessary and sufficient condition for asymptotic stability of trivial steady state in the absence of delay is derived. Then a delay dependent sufficient condition for local asymptotic stability of trivial, steady state and sufficient condition for no stability switching of trivial steady for such a network are derived. Numerical simulation results of the model were presented. Conclusion/Recommendations: From numerical simulation, it appears that there may be a possibility of multiple steady states of the model. It may be possible to investigate the condition for the existence of periodic solutions of the non-linear model analytically.
© 2010 Poulami D. Gupta, N. C. Majee and A. B. Roy. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.