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New Results on Periodicity of Non-autonomous Inertial Neural Networks Involving Non-reduced Order Method

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Abstract

This article mainly explores a class of non-autonomous inertial neural networks with time-varying delays and coefficients. By combining Lyapunov function method with differential inequality approach, some novel assertions are gained to guarantee the existence and exponential stability of periodic solutions for the addressed model. An example and its numerical simulations are given to support the proposed approach. The obtained results play an important role in designing the inertial neural networks and complement the earlier publications.

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References

  1. Babcock K, Westervelt R (1986) Stability and dynamics of simple electronic neural networks with added inertia. Phys D 23:464–469

    Article  Google Scholar 

  2. Babcock K, Westervelt R (1987) Dynamics of simple electronic neural networks. Phys D 28:305–316

    Article  MathSciNet  Google Scholar 

  3. Ke Y, Miao C (2013) Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays. Neurocomputing 117:196–205

    Article  Google Scholar 

  4. Yu S, Zhang Z, Quan Z (2015) New global exponential stability conditions for inertial Cohen–Grossberg neural networks with time delays. Neurocomputing 151:1446–1454

    Article  Google Scholar 

  5. Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151:1316–1326

    Article  Google Scholar 

  6. Wang J, Chen X, Huang L (2019) The number and stability of limit cycles for planar piecewise linear systems of node-saddle type. J Math Anal Appl 469(1):405–427

    Article  MathSciNet  MATH  Google Scholar 

  7. Ke Y, Miao C (2013) Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Comput Appl 23:1089–1099

    Article  Google Scholar 

  8. Ke Y, Miao C (2017) Anti-periodic solutions of inertial neural networks with time delays. Neural Process Lett 45:523–538

    Article  Google Scholar 

  9. Xu C, Zhang Q (2015) Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay. Neurocomputing 153:108–116

    Article  Google Scholar 

  10. Ge J, Xu J (2012) Weak resonant double Hopf bifurcations in an inertial four-neuron model with time delay. Int J Neural Syst 22:63–75

    Article  Google Scholar 

  11. Li C, Chen G, Liao L, Yu J (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B 41:337–343

    Article  Google Scholar 

  12. Liu Q, Liao X, Liu Y, Zhou S, Guo S (2009) Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn 58:573–609

    Article  MathSciNet  MATH  Google Scholar 

  13. Song Z, Xu J, Zhen B (2015) Multi-type activity coexistence in an inertial two-neuron system with multiple delays. Int J Bifurc Chaos 25(1530040):1–18

    Google Scholar 

  14. Wheeler D, Schieve W (1997) Stability and chaos in an inertial two-neuron system. Phys D 105:267–284

    Article  MATH  Google Scholar 

  15. Huang C, Cao J, Cao JD (2016) Stability analysis of switched cellular neural networks: a mode-dependent average dwell time approach. Neural Netw 82:84–99

    Article  Google Scholar 

  16. Tu Z, Cao J, Alsaedi A, Alsaadi F (2017) Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw 88:125–133

    Article  Google Scholar 

  17. Huang C, Hang H (2019) Periodicity of nonautonomous inertial neural networks involving proportional delays and nonreduced order method. Int J Biomath 12(2):1950016

    Article  MathSciNet  Google Scholar 

  18. Tu Z, Cao J, Hayat T (2016) Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks. Neural Netw 75:47–55

    Article  MATH  Google Scholar 

  19. Cai Z, Huang J, Huang L (2018) Periodic orbit analysis for the delayed Filippov system. Proc Am Math Soc 146(11):4667–4682

    Article  MathSciNet  MATH  Google Scholar 

  20. Huang C, Yang Z, Yi T, Zou X (2014) On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities. J Differ Equ 256:2101–2114

    Article  MathSciNet  MATH  Google Scholar 

  21. Prakash M, Balasubramaniam P, Lakshmanan S (2016) Synchronization of Markovian jumping inertial neural networks and its applications in image encryption. Neural Netw 83:86–93

    Article  Google Scholar 

  22. Wang J, Huang C, Huang L (2019) Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type. Nonlinear Anal Hybrid Syst 33:162–178

    Article  MathSciNet  Google Scholar 

  23. Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization analysis of inertialmemristive neural networks with time delays. Cogn Neurodyn 10:437–451

    Article  Google Scholar 

  24. Li X, Li X, Hu C (2017) Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw 96:91–100

    Article  Google Scholar 

  25. Huang C, Liu B (2019) New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325:283–287

    Article  Google Scholar 

  26. Hale JK, VerduynLunel SM (1993) Introduction to functional differential equations. Springer, New York

    Book  Google Scholar 

  27. Liu B (2017) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Meth Appl Sci 40:167–174

    Article  MathSciNet  MATH  Google Scholar 

  28. Wu Y, Cao J, Alo A, Abdullah AM, Elaiw A (2015) Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay. Neural Netw 69:135–143

    Article  MATH  Google Scholar 

  29. Wu Y, Cao J, Li Q, Alsaedi A, Alsaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139

    Article  Google Scholar 

  30. Li Q, Guo J, Sun C, Wu Y, Ding Z (2019) Finite-time synchronization for a class of dynamical complex networks with nonidentical nodes and uncertain disturbance. J Syst Sci Complex online, https://doi.org/10.1007/s11424-018-8141-5

  31. Li YY (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46:59–69

    Article  Google Scholar 

  32. Li YY, Lou JG, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Franklin Inst 355:6520–6530

    Article  MathSciNet  MATH  Google Scholar 

  33. Duan L, Shi M, Wang Z, Huang L (2019) Global exponential synchronization of delayed complex-valued recurrent neural networks with discontinuous activations. Neural Process Lett. https://doi.org/10.1007/s11063-018-09970-8

    Google Scholar 

  34. Duan L, Wei H, Huang L (2019) Finite-time synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Fuzzy Sets Syst 361:56–70

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of our original paper. This work was supported by the National Natural Science Foundation of China (Nos.11861037, 71471020, 51839002), the Hunan Provincial Natural Science Foundation of China(No. 2016JJ1001), the Scientific Research Fund of Hunan Provincial Education Department(No. 15A003) and the Zhejiang Provincial Natural Science Foundation of China (Grant no.LY18A010019).

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Correspondence to Bingwen Liu.

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Huang, C., Yang, L. & Liu, B. New Results on Periodicity of Non-autonomous Inertial Neural Networks Involving Non-reduced Order Method. Neural Process Lett 50, 595–606 (2019). https://doi.org/10.1007/s11063-019-10055-3

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