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Existence of Periodic Solutions to Non-autonomous Delay Cohen-Grossberg Neural Networks with Impulses on Time Scales

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Advances in Neural Networks – ISNN 2016 (ISNN 2016)

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Abstract

In this paper, without assuming the boundedness of activation functions, by applying continuous theorem of coincidence degree theory and the theory of calculus on time scales, we obtain some criteria for the existence exponential stability of periodic solutions to impulses Cohen-Grossberg neural networks with delay on time scales. Finally, an example is given to illustrate our results.

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References

  1. Cohen, M., Grossberg, S.: Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815–816 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao, J., Song, Q.: Stability in cohen-grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19, 1601–1617 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, Z., Ruan, J.: Global stability analysis of impulsive cohen-grossberg neural networks with delay. Phys. Lett. A 345, 101–111 (2005)

    Article  MATH  Google Scholar 

  4. Xiang, H., Cao, J.: Almost periodic solution of cohen-grossberg neural networks with bounded and unbounded delays. Nonlinear Anal. Real World Appl. 10(4), 2407–2419 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, Y.: Existence and Stability of Periodic Solutions for Cohen-Grossberg Neural Networks with Multiple Delays. Chaos Solitons Fractals 20, 459–466 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li, C., Li, Y., Ye, Y.: Exponential stability of fuzzy cohen-grossberg neural networks with time delays and impulsive effects. Commun. Nonlinear Sci. Numer. Simul. 15(11), 3599–3606 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, Y.: Almost automorphic solution for neutral type high-order hopfield neural networks with delays inleakage terms on time scale. Appl. Math. Comput. 242, 679–693 (2014)

    MathSciNet  MATH  Google Scholar 

  8. 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, 1621–1630 (2009)

    Article  Google Scholar 

  9. Li, Y., Wang, C.: Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales. Adv. Differ. Eqn. 77 (2012)

    Google Scholar 

  10. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser, Boston (2001)

    Book  MATH  Google Scholar 

  11. Yang, Z., Xu, D.: Impulsive effects on stability of cohen-grossberg neural networks with variable delays. Appl. Math. Comput. 177(1), 63–78 (2006)

    MathSciNet  MATH  Google Scholar 

  12. Li, Y.: Periodic solutions of non-autonomous cellular neural networks with impulses and delays on time scales. IMA J. Math. Control Inf. 13, 273–291 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lakshmikantham, V., Vatsala, A.S.: Hybird systems on time scales. J. Comput. Appl. Math. 141, 227–235 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kaufmann, E., Raffoul, Y.: Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J. Math. Anal. Appl. 319(1), 315–325 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Agarwal, R., Bohner, M., Peterson, A.: Inequalities on times scales: a survey. Math. Inequalities Appl. 4(4), 535–557 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gong, W., Liang, J., Cao, J.: Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw. 70, 81–89 (2015)

    Article  Google Scholar 

  17. Cho, Y.J., Chen, Y.Q.: Topological Degree Theory and Application. Taylor & Francis Group, Boca Raton, London, New York (2006)

    Google Scholar 

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Acknowledgments

This work is supported by the National Natural Sciences Foundation of Peoples Republic of China under Grant 11561070, and the Natural Scientific Research Fund Project of Yunnan Province (No. 2014FD049), and the Young Teacher Program of Yuxi Normal University.

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Authors and Affiliations

  1. Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan, 653100, China

    Zhouhong Li

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  1. Zhouhong Li
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Correspondence to Zhouhong Li .

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Editors and Affiliations

  1. The Chinese Academy of Sciences, Beijing, China

    Long Cheng

  2. Huazhong University of Science and Tech., Wuhan, Jiangsu, China

    Qingshan Liu

  3. Russian Academy of Sciences, SPIIRAS, St. Petersburg, Russia

    Andrey Ronzhin

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Li, Z. (2016). Existence of Periodic Solutions to Non-autonomous Delay Cohen-Grossberg Neural Networks with Impulses on Time Scales. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_25

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  • DOI: https://doi.org/10.1007/978-3-319-40663-3_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40662-6

  • Online ISBN: 978-3-319-40663-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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