Research Article Open Access

Stability Analysis of a Class of Three-Neuron Delayed Cellular Neural Network

Poulami Das Gupta1, N. C. Majee1 and A. B. Roy2
  • 1 Jadavpur University, India
  • 2 Jadavpur University,

Abstract

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.

OnLine Journal of Biological Sciences
Volume 10 No. 1, 2010, 36-43

DOI: https://doi.org/10.3844/ojbsci.2010.36.43

Submitted On: 25 December 2009 Published On: 30 June 2010

How to Cite: Gupta, P. D., Majee, N. C. & Roy, A. B. (2010). Stability Analysis of a Class of Three-Neuron Delayed Cellular Neural Network. OnLine Journal of Biological Sciences, 10(1), 36-43. https://doi.org/10.3844/ojbsci.2010.36.43

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Keywords

  • Cellular neural network
  • asymptotic stability
  • delay dependent stability
  • delay independent stability switching