Abstract
In this paper we present and study a ring neural network model with delays. We study existence and uniqueness of equilibrium point and global stability of the model system. At the end few examples have been given to illustrate the analytical findings.
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References
Pan, L., Cao, J.: Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal. Real World Appl. 12(6), 3014–3027 (2011)
Xiang, H., Cao, J.: Almost periodic solutions of recurrent neural networks with continuously distributed delays. Nonlinear Anal. 71(12), 6097–6108 (2009)
Yang, Y., Cao, J.: Stability and periodicity in delayed cellular neural networks with impulsive effects. Nonlinear Anal. Real World Appl. 8(1), 362–374 (2007)
Cao, J., Liang, J.: Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J. Math. Anal. Appl. 296(2), 665–685 (2004)
Abbas, S., Xia, Y.: Existence and attractivity of k-almost automorphic sequence solution of a model of cellular neural networks with delay. Acta Math. Sci. Ser. B Engl. Ed. 33(1), 290–302 (2013)
Abbas, S.: Existence and attractivity of k-pseudo almost automorphic sequence solution of a model of bidirectional neural networks. Acta Appl. Math. 119, 57–74 (2012)
Abbas, S.: Pseudo almost periodic sequence solutions of discrete time cellular neural networks. Nonlinear Anal. Model. Control 14(3), 283–301 (2009)
Gao, B., Zhang, W.: Equilibria and their bifurcations in a recurrent network involving iterates of a transcendental function. IEEE Trans. Neural Netw. 19(5), 782–794 (2008)
Baldi, P., Atiya, A.F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5(4), 612–621 (1994)
Feng, C., Plamondon, R.: An oscillatory criterion for a delayed neural ring network model. Neural Netw. 29–30, 70–79 (2012)
Wei, J., Zhang, C.: Bifurcation analysis of a class of neural networks with delays. Nonlinear Anal: Real World Appl. 9, 2234–2252 (2008)
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Tyagi, S., Abbas, S., Ray, R.K. (2015). Stability Analysis of an Integro Differential Equation Model of Ring Neural Network with Delay. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_3
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DOI: https://doi.org/10.1007/978-81-322-2485-3_3
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