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Original Articles

Existence and p-exponential stability of periodic solution for stochastic shunting inhibitory cellular neural networks with time-varying delays

, &
Pages 945-956 | Received 31 Oct 2014, Accepted 20 Jun 2016, Published online: 28 Sep 2016

References

  • J. Gao, Q.R. Wang, L.W. Zhang, Existence and stability almost periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales, Applied Mathematics and Computation, 237 (2014) 639–649. doi: 10.1016/j.amc.2014.03.051
  • B.W. Liu, J.Y. Shao, Almost periodic solutions for SICNNs with time-varying delays in the leakage terms, Jouranl of Inequalities and Applications, 494 (2013) 1–22.
  • B.W. Liu, Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays, Neurocomputing, 148 (2015) 445–454. doi: 10.1016/j.neucom.2014.07.020
  • B. Armmar, F. Chérif, A.M. Alimi, Existence and uniqueness of pseudo almost periodic solutions of re-current neural networks with time-varying coefficients and mixed delays, IEEE Transactions on Neural Networks and Learning Systems, 23 (2012) 109–118. doi: 10.1109/TNNLS.2011.2178444
  • S. Abbas, Y.H. Xia, Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument, Neural Process Letters, 2014, in press.
  • Y.K. Li, J.Y. Shu, Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales, Communications in Nonlinear Science and Numerical Simulation, 11 (2011) 137–150.
  • H.H. Wu, Pseudo almost periodic solution of shunting inhibitroy cellular neural networks with delay, Journal of Applied Mathematics, Volume 2011, Article ID 510789, 14 pages.
  • W.T. Wang, B.W. Liu, Global exponential stability of pseudo almost periodic solutions for SICNNs with time-varying leakage delays, Abstract and Applied Analysis, Volume 2014, Article ID 967328, 17 pages.
  • B.W. Liu, Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays, Neural Process Letters, 42 (2015) 233–256. doi: 10.1007/s11063-014-9354-9
  • L.Q. Peng, W.T. Wang, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms, Neurocomputing, 111 (2013) 27–33. doi: 10.1016/j.neucom.2012.11.031
  • B.W. Liu, New convergence behavior of solutions to shunting inhibitory cellular neural networks with unbounded delays and time-varying coefficients, Applied Mathematical Modelling, 33 (2009) 54–60. doi: 10.1016/j.apm.2007.10.009
  • Y.H. Xia, J.D. Cao, Z.K. Huang, Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos, Solitons & Fractals, 34 (2007) 1599–1607. doi: 10.1016/j.chaos.2006.05.003
  • B.W. Liu, L.H. Huang, Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Chaos, Solitons & Fractals, 31 (2007) 211–217. doi: 10.1016/j.chaos.2005.09.052
  • C.J. Xu, Q.M. Zhang, On anti-periodic solutions of a shunting inhibitory cellular neural networks with distributed delays, Journal of Applied Mathematics and Computing, 47 (2015) 1–13. doi: 10.1007/s12190-014-0757-6
  • S. Haykin, Neural Networks, Prentice-Hall, NJ, 1994.
  • S. Blythe, X. Mao, X. Liao, Stability of stochastic delay neural networks, Journal of the Franklin Institute, 338 (2001) 481–495.
  • B. Tojtovska, S. Janković, On some stability problems of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, Applied Mathematics and Computation, 239 (2014) 211–226. doi: 10.1016/j.amc.2014.04.038
  • J. Li, M.F. Hu, L.X. Guo, Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays, Neurocomputing, 138 (2014) 92–98. doi: 10.1016/j.neucom.2014.02.042
  • Y.C. Shi, P.Y. Zhu, Asymptotic stability analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, Applied Mathematics and Computation, 242 (2014) 159–167. doi: 10.1016/j.amc.2014.05.056
  • Q.X. Zhu, J.D. Cao, Mean-square exponential inputto-state stability of stochastic delayed neural networks, Neurocomputing, 131 (2014) 157–163. doi: 10.1016/j.neucom.2013.10.029
  • A. Meyer-Bäse, G. Botella, L.R. Rusinek, Stochastic stability analysis of competitive neural networks with different time-scales, Neurocomputing, 118 (2013) 115–118. doi: 10.1016/j.neucom.2013.02.020
  • D.S. Li, X.H. Wang, D.Y. Xu, Existence and global p-exponential stability of periodic solution for impulsive stochastic neural networks with delays, Nonlinear Analysis: Hybrid Systems, 6 (2012) 847–858.
  • R. Khasminskii, Stochastic Stability of Differential Equations, Stochastic Modelling and Applied Probability, vol. 66. Springer, Berlin, 2012.
  • D.Y. Xu, Y.M. Huang, Z.G. Yang, Existence theorems for periodic Markov process and stochastic functional differential equations, Discrete and Continuous Dynamical Systems, 24 (2009) 1005–1023. doi: 10.3934/dcds.2009.24.1005
  • F.K. Wu, S.G. Hu, Y. Liu, Positive solution and its asymptotic behavior of stochastic functional Kolmogorov-type system, Journal of Mathematical Analysis and Applications, 364 (2010) 104–118. doi: 10.1016/j.jmaa.2009.10.072
  • L. Yang, Y.K. Li, Periodic solutions for stochastic shunting inhibitory cellular neural networks with distributed delays, Advances in Difference Equations, 37 (2014) d1–14.
  • W.R. Zhao, H.S. Zhang, On almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients and time-varying delays, Nonlinear Analysis: Real World Applications, 9 (2008) 2326–2336. doi: 10.1016/j.nonrwa.2007.05.015
  • Y.F. Weng, L. Ju, J. Wang, Cellular neural networks and Biological visual information processing model, Journal of Beijing Technology and Business University (Natural Science Edition), 25 (2007) 42–58.
  • C.J. Xu, Q.M. Zhang, Y.S. Wu, Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays, Network: Computation in Neural Systems, 25 (2014) 168–192.
  • J. TØnesen, Optogenetic cell control in experimental models of neurological disorders, Behavioural Brain Research, 255 (2013) 35–43. doi: 10.1016/j.bbr.2013.07.007
  • P. Gerlee, A.R.A. Anderson, Modelling evolutionary cell behaviour using neural networks: Application to tumour growth, Biosystems, 95 (2009) 166–174. doi: 10.1016/j.biosystems.2008.10.007
  • M. Moghtadaei, M.R.H, Golpayegani, R. Malekzadeh, A variable structure fuzzy neural network model of squamous dysplasia and esophageal squamous cell carcinoma based on a global chaotic optimization algorithm. Journal of Theoretical Biology, 318 (2013) 164–172. doi: 10.1016/j.jtbi.2012.11.013

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