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Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect

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Abstract

This paper investigates the fixed-time synchronization problems for competitive neural networks with proportional delays and impulsive effect. The concerned network involves two coupling terms, i.e., long-term memory and short-term memory, which leads to the difficulty to the dynamics analysis. Based on Lyapunov functionals, the differential inequalities and for the objective of making the settling time independent of initial condition, a novel criterion guaranteeing the fixed-time synchronization of addressed system is derived. Finally, two examples and their simulations are given to demonstrate the effectiveness of the obtained results.

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References

  1. Alimi AM, Aouiti C, Chérif F, Dridi F, M’hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing. https://doi.org/10.1016/j.neucom.2018.01.061

    Article  Google Scholar 

  2. Aouiti C, Assali EA, Gharbia IB, El Foutayeni Y (2019) Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations. Neurocomputing 357:292–309

    Article  Google Scholar 

  3. Rajchakit G, Saravanakumar R (2016) Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2461-y

    Article  Google Scholar 

  4. Ma Y, Zheng Y (2016) Delay-dependent stochastic stability for discrete singular neural networks with Markovian jump and mixed time-delays. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2414-5

    Article  Google Scholar 

  5. Asproulis N, Drikakis D (2013) An artificial neural network-based multiscale method for hybrid atomistic-continuum simulations. Microfluidics Nanofluidics 15(4):559–574

    Article  Google Scholar 

  6. Asproulis N, Drikakis D (2009) Nanoscale materials modelling using neural networks. J Comput Theoret Nanosci 6(3):514–518

    Article  Google Scholar 

  7. Asproulis N, Kalweit M, Drikakis D (2012) A hybrid molecular continuum method using point wise coupling. Adv Eng Softw 46(1):85–92

    Article  Google Scholar 

  8. Kalweit M, Drikakis D (2008) Coupling strategies for hybrid molecular-continuum simulation methods. Proc Inst Mech Eng Part C J Mech Eng Sci 222(5):797–806

    Article  Google Scholar 

  9. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 5:815–826

    Article  MathSciNet  Google Scholar 

  10. Meyer-Bäse A, Ohl F, Scheich H (1996) Singular perturbation analysis of competitive neural networks with different time scales. Neural Comput 8(8):1731–1742

    Article  Google Scholar 

  11. Hopfield J (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554–2558

    Article  MathSciNet  Google Scholar 

  12. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci 81(10):3088–3092

    Article  Google Scholar 

  13. Grossberg S (1976) Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors. Biol Cybern 23(3):121–134

    Article  MathSciNet  Google Scholar 

  14. Amari SI (1983) Field theory of self-organizing neural nets. IEEE Trans Syst Man Cybern 5:741–748

    Article  MathSciNet  Google Scholar 

  15. Lou X, Cui B (2007) Synchronization of competitive neural networks with different time scales. Phys A 380:563–576

    Article  Google Scholar 

  16. Gu H (2009) Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation. Neurocomputing 73:350–356

    Article  Google Scholar 

  17. Gan Q, Hu R, Liang Y (2012) Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays. Commun Nonlinear Sci Numer Simul 17:3708–3718

    Article  MathSciNet  Google Scholar 

  18. Aouiti C, Gharbia IB, Cao J, M’hamdi MS, Alsaedi A (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111–127

    Article  MathSciNet  Google Scholar 

  19. Aouiti C, M’hamdi MS, Chérif F, Alimi AM (2017) Impulsive generalised high-order recurrent neural networks with mixed delays: stability and periodicity. Neurocomputing. https://doi.org/10.1016/j.neucom.2017.11.037

    Article  Google Scholar 

  20. Aouiti C, Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing. https://doi.org/10.1016/j.neucom.2017.04.048

    Article  Google Scholar 

  21. Li X (2009) Existence and global exponential stability of periodic solution for impulsive Cohen–Grossberg-type BAM neural networks with continuously distributed delays. Appl Math Comput 215(1):292–307

    MathSciNet  MATH  Google Scholar 

  22. Aouiti C, M’hamdi MS, Cao J, Alsaedi A (2017) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648

    Article  Google Scholar 

  23. Aouiti C, M’hamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140

    Article  Google Scholar 

  24. Aouiti C, Assali EA, Gharbia IB (2019) Pseudo almost periodic solution of recurrent neural networks with D operator on time scales. Neural Process Lett 50(1):297–320

    Article  Google Scholar 

  25. Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cognit Neurodyn 10(6):573–591

    Article  MathSciNet  Google Scholar 

  26. Mhamdi MS, Aouiti C, Touati A, Alimi AM, Snasel V (2016) Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci 36(6):1662–1682

    Article  MathSciNet  Google Scholar 

  27. Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2558-3

    Article  Google Scholar 

  28. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23(7):1709

    Article  MathSciNet  Google Scholar 

  29. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I Regul Pap 52(2):417–426

    Article  MathSciNet  Google Scholar 

  30. Zhou L, Zhao Z (2016) Exponential stability of a class of competitive neural networks with multi-proportional delays. Neural Process Lett 44(3):651–663

    Article  Google Scholar 

  31. Abdurahman A, Jiang H, Teng Z (2016) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111

    Article  MathSciNet  Google Scholar 

  32. Wang W (2017) Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2017.04.005

    Article  Google Scholar 

  33. Li Y, Yang X, Shi L (2016) Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations. Neurocomputing 185:242–253

    Article  Google Scholar 

  34. Duan L, Fang X, Yi X, Fu Y (2017) Finite-time synchronization of delayed competitive neural networks with discontinuous neuron activations. Int J Mach Learn Cybern 9(10):1649–1661

    Article  Google Scholar 

  35. Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60(3):032201

    Article  MathSciNet  Google Scholar 

  36. Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    Article  MathSciNet  Google Scholar 

  37. Li H, Li C, Huang T, Zhang W (2018) Fixed-time stabilization of impulsive Cohen–Grossberg BAM neural networks. Neural Netw 98:203–211

    Article  Google Scholar 

  38. Meyer-Baese A, Pilyugin SS, Chen Y (2003) Global exponential stability of competitive neural networks with different time scales. IEEE Trans Neural Netw 14(3):716–719

    Article  Google Scholar 

  39. Gong S, Yang S, Guo Z, Huang T (2019) Global exponential synchronization of memristive competitive neural networks with time-varying delay via nonlinear control. Neural Process Lett 49(1):103–119

    Article  Google Scholar 

  40. Yang X, Cao J, Long Y, Rui W (2010) Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations. IEEE Trans Neural Netw 21(10):1656–1667

    Article  Google Scholar 

  41. Sader M, Abdurahman A, Jiang H (2019) General decay lag synchronization for competitive neural networks with constant delays. Neural Process Lett 50(1):445–457

    Article  Google Scholar 

  42. Duan L, Zhang M, Zhao Q (2019) Finite-time synchronization of delayed competitive neural networks with different time scales. J Inf Optim Sci 40(4):813–837

    MathSciNet  Google Scholar 

  43. Yang F, Mei J, Wu Z (2016) Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control. IET Control Theory Appl 10(14):1630–1640

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program [grant number R.G.P.1/129/40].

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Authors and Affiliations

  1. Faculty of Sciences of Bizerta, Department of Mathematics, Research Units of Mathematics and Applications UR13ES47, University of Carthage, BP, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & El Abed Assali

  2. Department of Mathematics, College of Science, King Khalid University, Abha, 9004, Saudi Arabia

    Farouk Chérif

  3. MaPSFA-ESST Hammam Sousse, ISSAT, University of Sousse, Sousse, Tunisia

    Farouk Chérif & Anis Zeglaoui

  4. LAMMDA-ESST Hammam Sousse, University of Sousse, Sousse, Tunisia

    Anis Zeglaoui

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  1. Chaouki Aouiti
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  2. El Abed Assali
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  3. Farouk Chérif
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  4. Anis Zeglaoui
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Correspondence to Chaouki Aouiti.

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Aouiti, C., Assali, E., Chérif, F. et al. Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect. Neural Comput & Applic 32, 13245–13254 (2020). https://doi.org/10.1007/s00521-019-04654-3

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  • DOI: https://doi.org/10.1007/s00521-019-04654-3

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