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Periodic Solution for \(\nabla \)-Stochastic High-Order Hopfield Neural Networks with Time Delays on Time Scales

  • Li Yang
  • Yu Fei
  • Wanqin Wu
Article
  • 22 Downloads

Abstract

In this paper, the comparison theorem and Gronwall’s inequality with \(\nabla \)-derivative on time scales are constructed. Based on \(\nabla \)-stochastic integration, the \(\nabla \)-stochastic high-order Hopfield neural networks with time delays on time scales is introduced and studied. By using contraction mapping principal and differential inequality technique on time scales, some sufficient conditions for the existence and exponential stability of periodic solutions for a class of \(\nabla \)-stochastic high-order Hopfield neural networks with time delays on time scales are established. Our results show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors for periodicity. Finally, a numerical example is provided to illustrate the feasibility of our results. The results of this paper are completely new even if the time scale \(\mathbb {T}=\mathbb {R}\) or \(\mathbb {Z}\).

Keywords

Stochastic neural networks Periodic solutions Exponential stability Time scales 

Mathematics Subject Classification

34N05 34K13 34K20 92B20 

Notes

Acknowledgements

All authors would like to express their sincere thanks to the editor for handling this paper during reviewing process and to the referees for suggesting some corrections to help making the content of the paper more accurate.

Author Contributions

All authors contributed to the manuscript and typed, read and approved the final manuscript.

Compliance with Ethical Standards

Conflict of interest

All authors declare that they have no competing interests.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Statistics and MathematicsYunnan University of Finance and EconomicsKunmingPeople’s Republic of China
  2. 2.Department of OrganizationYunnan Nationalities UniversityKunmingPeople’s Republic of China

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