Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

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Abstract

By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

Abstract

By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

References

  • 1. Arik, S.; Orman, Z. - Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Physics Letters A, 341 (2005), 410-421.

  • 2. Bai, C. - Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses, Chaos Solitons Fractals, 35 (2008), 263-267.

  • 3. Bi, Li; Bohner, M.; Fan, M. - Periodic solutions of functional dynamic equations with infinite delay, Nonlinear Anal., 68 (2008), 1226-1245.

  • 4. Bohner, M.; Fan, M.; Zhang, J. - Existence of periodic solutions in predator- prey and competition dynamic systems, Nonlinear Anal. Real World Appl., 7 (2006), 1193-1204.

  • 5. Bohner, M.; Peterson, A. - Advances in Dynamic Equations on Time Scales, Birkh¨auser Boston, Inc., Boston, MA, 2003.

  • 6. Bohner, M.; Peterson, A. - Dynamic Equations on Time Scales. An Introduction with Applications, Birkh¨auser Boston, Inc., Boston, MA, 2001.

  • 7. Cao, J.; Liang, J. - Boundedness and stability for Cohen-Grossberg neural network with time-varying delays, J. Math. Anal. Appl., 296 (2004), 665-685.

  • 8. Cao, J.; Li, X. - Stability in delayed Cohen-Grossberg neural networks: LMI opti- mization approach, Phys. D, 212 (2005), 54-65.

  • 9. Chen, T.; Rong, L. - Delay-independent stability analysis of Cohen-Grossberg neural networks, Phys. Lett. A, 317 (2003), 436-449.

  • 10. Chen, Z.; Ruan, J. - Global dynamic analysis of general Cohen-Grossberg neural networks with impulse, Chaos Solitons Fractals, 32 (2007), 1830-1837.

  • 11. Cohen, M.A.; Grossberg, S. - Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826.

  • 12. Huang, T. - Exponential stability of fuzzy cellular neural networks with distributed delay, Physics Lett. A, 351 (2006), 48-52.

  • 13. Huang, T. - Exponential stability of delayed fuzzy cellular neural networks with diffusion, Chaos Solitons Fractals, 31 (2007), 658-664.

  • 14. Kaufmann, E.R.; Raffoul, Y.N. - Periodic solutions for a neutral nonlinear dy- namical equation on a time scale, J. Math. Anal. Appl., 319 (2006), 315-325.

  • 15. Lakshmikantham, V.; Vatsala, A.S. - Hybrid systems on time scales. Dynamic equations on time scales, J. Comput. Appl. Math., 141 (2002), 227-235.

  • 16. Li, Y.; Zhao, L.; Zhang, T. - Global exponential stability and existence of periodic solution of impulsive Cohen-Grossberg neural networks with distributed delays on time scales, Neural Process Lett., 33 (2011), 61-81.

  • 17. Li, Y.; Gao, S. - Global exponential stability for impulsive BAM neural networks with distributed delays on time scales, Neural Process Lett., 31 (2010), 65-91.

  • 18. Li, Y.; Chen, X. Zhao, L. - Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing, 72 (2009), 1621-1630.

  • 19. Liang, J.; Cao, J. - Global output convergence of recurrent neural networks with distributed delays, Nonlinear Anal. Real World Appl., 8 (2007), 187-197.

  • 20. Lu, W.; Chen, T. - New conditions on global stability of Cohen-Grossberg neural networks, Neural Computation, 15 (2003), 1173-1189.

  • 21. O’Regan, D.; Cho, Y.J.; Chen, Y. - Topological Degree Theory and Applications, Series in Mathematical Analysis and Applications, 10, Chapman & Hall/CRC, Boca Raton, FL, 2006.

  • 22. Song, Q.; Cao, J. - Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays, J. Comput. Appl. Math., 197 (2006), 188-203.

  • 23. Song, Q.; Zhang, J. - Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays, Nonlinear Anal. RealWorld Appl., 9 (2008), 500-510.

  • 24. Song, Q.; Wang, Z. - Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, Physica A, 387 (2008), 3314-3326.

  • 25. Wang, L.; Zou, X. - Harmless delays in Cohen-Grossberg neural networks, Phys. D, 170 (2002), 162-173.

  • 26. Yang, T.; Yang, L. - The global stability of fuzzy cellular neural network, IEEE Trans. Circuits Systems I Fund. Theory Appl., 43 (1996), 880-883.

  • 27. Yang, T.; Yang, L.; Wu, C.; Chua, L. - Fuzzy cellular neural networks: theory, In Proc. of IEEE Int. Workshop on Cellular Neural Networks Appl., 1996, 181-186.

  • 28. Yang, T.; Yang, L.: Wu, C.; Chua, L. - Fuzzy cellular neural networks: appli- cations, In Proc. of IEEE Int. Workshop on Cellular Neural Neworks Appl., 1996, 225-230.

  • 29. Ye, H.; Michel, A.N.; Wang, K. - Qualitative analysis of Cohen-Grossberg neural networks with multiple delays, Phys. Rev. E, 51 (1995), part B, 2611-2618.

  • 30. Yuan, K.; Cao, J. - An analysis of global asymptotic stability of delayed Cohen- Grossberg neural networks via nonsmooth analysis, IEEE Trans. Circuits Syst. I Regul. Pap., 52 (2005), 1854-1861.

  • 31. Yuan, K.; Cao, J.; Deng, J. - Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays, Neurocomputing, 69 (2006), 1619-1627.

  • 32. Zhang, Q.; Xiang, R. - Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Phys. Lett. A, 372 (2008), 3971-3977.

1. Arik, S.; Orman, Z. - Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Physics Letters A, 341 (2005), 410-421.

2. Bai, C. - Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses, Chaos Solitons Fractals, 35 (2008), 263-267.

3. Bi, Li; Bohner, M.; Fan, M. - Periodic solutions of functional dynamic equations with infinite delay, Nonlinear Anal., 68 (2008), 1226-1245.

4. Bohner, M.; Fan, M.; Zhang, J. - Existence of periodic solutions in predator- prey and competition dynamic systems, Nonlinear Anal. Real World Appl., 7 (2006), 1193-1204.

5. Bohner, M.; Peterson, A. - Advances in Dynamic Equations on Time Scales, Birkh¨auser Boston, Inc., Boston, MA, 2003.

6. Bohner, M.; Peterson, A. - Dynamic Equations on Time Scales. An Introduction with Applications, Birkh¨auser Boston, Inc., Boston, MA, 2001.

7. Cao, J.; Liang, J. - Boundedness and stability for Cohen-Grossberg neural network with time-varying delays, J. Math. Anal. Appl., 296 (2004), 665-685.

8. Cao, J.; Li, X. - Stability in delayed Cohen-Grossberg neural networks: LMI opti- mization approach, Phys. D, 212 (2005), 54-65.

9. Chen, T.; Rong, L. - Delay-independent stability analysis of Cohen-Grossberg neural networks, Phys. Lett. A, 317 (2003), 436-449.

10. Chen, Z.; Ruan, J. - Global dynamic analysis of general Cohen-Grossberg neural networks with impulse, Chaos Solitons Fractals, 32 (2007), 1830-1837.

11. Cohen, M.A.; Grossberg, S. - Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826.

12. Huang, T. - Exponential stability of fuzzy cellular neural networks with distributed delay, Physics Lett. A, 351 (2006), 48-52.

13. Huang, T. - Exponential stability of delayed fuzzy cellular neural networks with diffusion, Chaos Solitons Fractals, 31 (2007), 658-664.

14. Kaufmann, E.R.; Raffoul, Y.N. - Periodic solutions for a neutral nonlinear dy- namical equation on a time scale, J. Math. Anal. Appl., 319 (2006), 315-325.

15. Lakshmikantham, V.; Vatsala, A.S. - Hybrid systems on time scales. Dynamic equations on time scales, J. Comput. Appl. Math., 141 (2002), 227-235.

16. Li, Y.; Zhao, L.; Zhang, T. - Global exponential stability and existence of periodic solution of impulsive Cohen-Grossberg neural networks with distributed delays on time scales, Neural Process Lett., 33 (2011), 61-81.

17. Li, Y.; Gao, S. - Global exponential stability for impulsive BAM neural networks with distributed delays on time scales, Neural Process Lett., 31 (2010), 65-91.

18. Li, Y.; Chen, X. Zhao, L. - Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing, 72 (2009), 1621-1630.

19. Liang, J.; Cao, J. - Global output convergence of recurrent neural networks with distributed delays, Nonlinear Anal. Real World Appl., 8 (2007), 187-197.

20. Lu, W.; Chen, T. - New conditions on global stability of Cohen-Grossberg neural networks, Neural Computation, 15 (2003), 1173-1189.

21. O’Regan, D.; Cho, Y.J.; Chen, Y. - Topological Degree Theory and Applications, Series in Mathematical Analysis and Applications, 10, Chapman & Hall/CRC, Boca Raton, FL, 2006.

22. Song, Q.; Cao, J. - Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays, J. Comput. Appl. Math., 197 (2006), 188-203.

23. Song, Q.; Zhang, J. - Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays, Nonlinear Anal. RealWorld Appl., 9 (2008), 500-510.

24. Song, Q.; Wang, Z. - Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, Physica A, 387 (2008), 3314-3326.

25. Wang, L.; Zou, X. - Harmless delays in Cohen-Grossberg neural networks, Phys. D, 170 (2002), 162-173.

26. Yang, T.; Yang, L. - The global stability of fuzzy cellular neural network, IEEE Trans. Circuits Systems I Fund. Theory Appl., 43 (1996), 880-883.

27. Yang, T.; Yang, L.; Wu, C.; Chua, L. - Fuzzy cellular neural networks: theory, In Proc. of IEEE Int. Workshop on Cellular Neural Networks Appl., 1996, 181-186.

28. Yang, T.; Yang, L.: Wu, C.; Chua, L. - Fuzzy cellular neural networks: appli- cations, In Proc. of IEEE Int. Workshop on Cellular Neural Neworks Appl., 1996, 225-230.

29. Ye, H.; Michel, A.N.; Wang, K. - Qualitative analysis of Cohen-Grossberg neural networks with multiple delays, Phys. Rev. E, 51 (1995), part B, 2611-2618.

30. Yuan, K.; Cao, J. - An analysis of global asymptotic stability of delayed Cohen- Grossberg neural networks via nonsmooth analysis, IEEE Trans. Circuits Syst. I Regul. Pap., 52 (2005), 1854-1861.

31. Yuan, K.; Cao, J.; Deng, J. - Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays, Neurocomputing, 69 (2006), 1619-1627.

32. Zhang, Q.; Xiang, R. - Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Phys. Lett. A, 372 (2008), 3971-3977.

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