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Dissipativity of a class of cellular neural networks with proportional delays

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Abstract

In this paper, the problem of dissipativity is investigated for cellular neural networks with proportional delays. Without assuming monotonicity, differentiability, and boundedness of activation functions, two new delay-independent criteria for checking the dissipativity of the addressed neural networks are established by using inner product properties and matrix theory. Two examples and their simulation results are given to show the effectiveness and less conservatism of the proposed criteria.

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References

  1. Zhang, Y., Pheng, A.H., Kwong, S.L.: Convergence analysis of cellular neural networks with unbounded delay. IEEE Trans. Circuits Syst. I 48(6), 680–687 (2001)

    Article  MATH  Google Scholar 

  2. Liao, X., Wang, J.: Global dissipativity of continuous-time recurrent neural networks with time delay. Phys. Rev. E 68(1), 06118 (2003)

    Article  MathSciNet  Google Scholar 

  3. Gilli, M., Corinto, F., Checco, P.: Periodic oscillations and bifurcations in cellular neural networks. IEEE Trans. Circuits Syst. I 51(4), 938–962 (2004)

    MathSciNet  Google Scholar 

  4. Zhang, Q., Wei, X.P., Xu, J.: Delay-depend exponential stability of cellular neural networks with time-varying delays. Appl. Math. Comput. 195(2), 402–411 (2005)

    MathSciNet  Google Scholar 

  5. Tang, Q., Wang, X.: Chaos control and synchronization of cellular neural network with delays based on OPNCL control. Chin. Phys. Lett. 27(3), 030508 (2010)

    Article  Google Scholar 

  6. Huang, X., Zhao, Z., Wang, Z., Li, Y.: Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94(10), 13–21 (2012)

    Article  Google Scholar 

  7. Arik, S.: On the global dissipativity neural networks with time delays. Phys. Lett. A 326(4), 126–132 (2004)

    Article  MATH  Google Scholar 

  8. Cao, J., Yuan, K., Ho, D.W.C., Lam, J.: Global point dissipativity of neural networks with mixed time-varying delays. Chaos 16(1), 013105 (2006)

    Article  MathSciNet  Google Scholar 

  9. Huang, Y., Xu, D., Yang, Z.: Dissipativity and periodic attractor for non-autonomous neural networks with time-varying delays. Neurocomputing 70(16–18), 2953–2958 (2007)

    Article  Google Scholar 

  10. Sun, Y., Cui, B.: Dissipativity analysis of neural networks with time-varying delays. Int. J. Autom. Comput. 5(3), 290–295 (2008)

    Article  MathSciNet  Google Scholar 

  11. Song, Q., Cao, J.: Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. Chaos 18(4), 043126 (2008)

    Article  MathSciNet  Google Scholar 

  12. Ma, Z., Lei, K.: Dissipativity of neural networks with impulsive and delays. In: Advanced Computer Theory and Engineering (ICACTE), 2010 3rd International Conference on Neural Networks, Chengdu, pp. V1:95–V1:98 (2010)

    Google Scholar 

  13. Feng, Z., Lam, J.: Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Trans. Neural Netw. 22(6), 976–981 (2011)

    Article  MathSciNet  Google Scholar 

  14. Song, Q.: Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays. Neurocomputing 74(5), 838–845 (2011)

    Article  Google Scholar 

  15. Wu, Z., Park, J.H., Su, H., Chu, J.: Dissipativity analysis of stochastic neural networks with time delays. Nonlinear Dyn. 70(1), 825–839 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wu, Z., Lam, J., Su, H., Chu, J.: Stability and dissipativity analysis of static neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 199–210 (2012)

    Article  Google Scholar 

  17. Muralisankar, S., Gopalakrishnan, N., Balasubramaniam, P.: An LMI approach for global robust dissipativity analysis of T-S fuzzy neural networks with interval time-varying delays. Expert Syst. Appl. 39(3), 3345–3355 (2012)

    Article  Google Scholar 

  18. Wu, Z., Park, J.H., Su, H., Chu, J.: Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties. Nonlinear Dyn. 69, 1323–1332 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhou, L.: On the global dissipativity of a class of cellular neural networks with multipantograph delays. Adv. Artif. Neural Syst. 2011, 941426 (2011)

    Google Scholar 

  20. Zhang, Y., Zhou, L.: Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron. Sin. 40(6), 1159–1163 (2012) (Chinese)

    Google Scholar 

  21. Zhou, L.: Delay-dependent exponential stability of cellular neural networks with multi-proportional delays. Neural Process. Lett. (2012). doi:10.1007/s11063-012-9271-8

    Google Scholar 

  22. Kato, T., Mcleod, J.B.: The functional-differential equation. Bull. Am. Math. Soc. 77(2), 891–937 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  23. Fox, L., Mayers, D.F.: On a functional differential equational. J. Inst. Math. Appl. 8(3), 271–307 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  24. Iserles, A.: The asymptotic behavior of certain difference equation with proportional delays. Comput. Math. Appl. 28(1–3), 141–152 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  25. Iserles, A.: On neural functional-differential equation with proportional delays. J. Math. Anal. Appl. 207(1), 73–95 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu, Y.K.: Asymptotic behavior of functional differential equations with proportional time delays. Eur. J. Appl. Math. 7(1), 11–30 (1996)

    Article  MATH  Google Scholar 

  27. Van, B., Marshall, J.C., Wake, G.C.: Holomorphic solutions to pantograph type equations with neural fixed points. J. Math. Anal. Appl. 295(2), 557–569 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  28. Tan, M.C.: Feedback stabilization of linear systems with proportional delay. Inf. Control 35(6), 690–694 (2006) (Chinese)

    Google Scholar 

  29. Gan, S.: Exact and discretized dissipativity of the pantograph equation. J. Comput. Math. 25(1), 81–88 (2007)

    MathSciNet  MATH  Google Scholar 

  30. Kao, Y., Gao, C.: Global exponential stability analysis for cellular neural networks with variable coefficients and delays. Neural Comput. Appl. 17(3), 291–296 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The project is supported by the National Science Foundation of China (No. 60974144), Tianjin Municipal Education commission (No. 20100813) and Foundation for Doctors of Tianjin Normal University (No. 52LX34).

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  1. School of Mathematics Science, Tianjin Normal University, Tianjin, 300387, China

    Liqun Zhou

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  1. Liqun Zhou
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Zhou, L. Dissipativity of a class of cellular neural networks with proportional delays. Nonlinear Dyn 73, 1895–1903 (2013). https://doi.org/10.1007/s11071-013-0912-x

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