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Piecewise Pseudo Almost Periodic Solutions of Generalized Neutral-Type Neural Networks with Impulses and Delays

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Abstract

This paper is concerned with the generalized neutral-type neural networks with impulses and delays. By applying the contraction mapping principle and generalized Gronwall–Bellman’s inequality, we employ a novel argument to establish new results on the existence, uniqueness and exponential stability of piecewise pseudo almost periodic solutions. Some corresponding results in the literature can be enriched and extended. Moreover, a numerical example is given to illustrate the effectiveness of our results.

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References

  1. Alonso AI, Hong J, Rojo J (1998) A class of ergodic solutions of differential equations with piecewise constant arguments. Dyn Syst Appl 7:561–574

    MathSciNet  MATH  Google Scholar 

  2. Gui ZJ, Ge WG, Yang XS (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364:267–273

    Article  Google Scholar 

  3. Hale J (1977) Theory of functional differential equations. Springer, New York

    Book  Google Scholar 

  4. Kong FC (2017) Positive piecewise pseudo-almost periodic solutions of first-order singular differential equations with impulses. J Fixed Point Theory Appl. https://doi.org/10.1007/s11784-017-0438-9.

    Article  MathSciNet  Google Scholar 

  5. Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulse differential equations. World Scientific, Singapore

    Book  Google Scholar 

  6. Liu YR, Wang ZD, Liu XH (2012) Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays. Neurocomputing 94:46–53

    Article  Google Scholar 

  7. Liu J, Zhang C (2013) Composition of piecewise pseudo almost periodic functions and applications to abstract impulsive differential equations. Adv Differ Equ 11:1–21

    MathSciNet  Google Scholar 

  8. Liu DY, Du Y (2015) New results of stability analysis for a class of neutral-type neural network with mixed time delays. Int J Mach Learn Cybern 6(4):555–566

    Article  Google Scholar 

  9. Li XD, O’Regan D, Akca H (2015) Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays. IMA J Appl Math 80(1):85–99

    Article  MathSciNet  Google Scholar 

  10. Liu BW (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  11. Liu BW (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256

    Article  Google Scholar 

  12. Liu BW, Tunç C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435

    Article  Google Scholar 

  13. Liu C, Liu WP, Yang Z (2016) Stability of neural networks with delay and variable-time impulses. Neurocomputing 171:1644–1654

    Article  Google Scholar 

  14. Li YK, Yang L, Li B (2016) Existence and stability of pseudo almost periodic solution for neutral type high-order hopfield neural networks with delays in leakage terms on time scales. Neural Process Lett 44(3):603–623

    Article  Google Scholar 

  15. Rakkiyappan R, Balasubramaniam P (2008) New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71:1039–1045

    Article  Google Scholar 

  16. Rakkiyappan R, Balasubramaniam P (2008) LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl Math Comput 204(1):317–324

    MathSciNet  MATH  Google Scholar 

  17. Samoilenko AM, Perestyuk NA (1995) Impulsive differential equations. World Scientific Publishing Corporation, Singapore

    Book  Google Scholar 

  18. Samli R, Arik S (2009) New results for global stability of a class of neutral-type neural systems with time delays. Appl Math Comput 210(2):564–570

    MathSciNet  MATH  Google Scholar 

  19. Stamov GT (2012) Almost periodic solutions of impulsive differential equations. Springer, Berlin

    Book  Google Scholar 

  20. Wang K, Zhu YL (2010) Stability of almost periodic solution for a generalized neutral-type neural networks with delays. Neurocomputing 73(16):3300–3307

    Article  Google Scholar 

  21. Wang XH, Li SY, Xu DY (2011) Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dyn 64(1):65–75

    Article  MathSciNet  Google Scholar 

  22. Wang C, Agarwal RP (2014) Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive \(\nabla \)-dynamic equations on time scales. Adv Differ Equ 2014:153

    Article  MathSciNet  Google Scholar 

  23. Wang C (2016) Piecewise pseudo almost periodic solution for impulsive non-autonomous high-order Hopfield neural networks with variable delays. Neurocomputing 171:1291–1301

    Article  Google Scholar 

  24. Xu CJ, Zhang QM, Wu YS (2014) Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays. Netw Comput Neural 25(4):168–192

    Article  Google Scholar 

  25. Xie D, Jiang YP (2016) Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 207:528–538

    Article  Google Scholar 

  26. Yang CB, Huang TZ (2013) New results on stability for a class of neural networks with distributed delays and impulses. Neurocomputing 111:115–121

    Article  Google Scholar 

  27. Zhang J, Gui ZJ (2009) Periodic solutions of nonautonomous cellular neural networks with impulses and delays. Nonlinear Anal Real World Appl 10(3):1891–1903

    Article  MathSciNet  Google Scholar 

  28. Zhao DL, Han D (2011) Stability of linear neutral differential equations with delays and impulses established by the fixed points method. Nonlinear Anal 74(18):7240–7251

    Article  MathSciNet  Google Scholar 

  29. Zheng CD, Wang Y, Wang ZS (2014) New stability results of neutral-type neural networks with continuously distributed delays and impulses. Int J Comput Math 91(9):1880–1896

    Article  MathSciNet  Google Scholar 

  30. Zhang CY (2003) Almost periodic type functions and ergodicity. Kluwer Academic/Science Press, Beijing

    Book  Google Scholar 

  31. Zhang CY (1995) Pseudo almost periodic solutions of some differential equations II. J Math Anal Appl 192:543–561

    Article  MathSciNet  Google Scholar 

  32. Zhang CY (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 151:62–76

    Article  MathSciNet  Google Scholar 

  33. Zhou QY (2016) Pseudo almost periodic solutions for SICNNs with leakage delays and complex deviating arguments. Neural Process Lett 44(2):375–386

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11471109, 11471278).

Funding was provided by Scientific Research Fund of Hunan Provincial Education Department (Grant No. 13A093).

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Authors and Affiliations

  1. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Fanchao Kong & Zhiguo Luo

  2. Mathematics and Computer Science College, Changsha University, Changsha, 410022, Hunan, People’s Republic of China

    Fanchao Kong

  3. College of Mathematics and Finance, Xiangnan University, Chenzhou, 423000, Hunan, People’s Republic of China

    Xiaoping Wang

Authors
  1. Fanchao Kong
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  2. Zhiguo Luo
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  3. Xiaoping Wang
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Correspondence to Fanchao Kong.

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Kong, F., Luo, Z. & Wang, X. Piecewise Pseudo Almost Periodic Solutions of Generalized Neutral-Type Neural Networks with Impulses and Delays. Neural Process Lett 48, 1611–1631 (2018). https://doi.org/10.1007/s11063-017-9758-4

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  • DOI: https://doi.org/10.1007/s11063-017-9758-4

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