Skip to main content
Erschienen in: Neural Processing Letters 1/2019

10.02.2018

Global Mittag-Leffler Synchronization for Fractional-Order BAM Neural Networks with Impulses and Multiple Variable Delays via Delayed-Feedback Control Strategy

verfasst von: Renyu Ye, Xinsheng Liu, Hai Zhang, Jinde Cao

Erschienen in: Neural Processing Letters | Ausgabe 1/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper is concerned with the global Mittag-Leffler synchronization schemes for the Caputo type fractional-order BAM neural networks with multiple time-varying delays and impulsive effects. Based on the delayed-feedback control strategy and Lyapunov functional approach, the sufficient conditions are established to ensure the global Mittag-Leffler synchronization, which are described as the algebraic inequalities associated with the network parameters. The control gain constants can be searched in a wider range following the proposed synchronization conditions. The obtained results are more general and less conservative. A numerical example is also presented to illustrate the feasibility and effectiveness of the theoretical results based on the modified predictor–corrector algorithm.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Podlubny I (1999) Fractional differential equations. Academic Press, New YorkMATH Podlubny I (1999) Fractional differential equations. Academic Press, New YorkMATH
2.
Zurück zum Zitat Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, AmsterdamMATH Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, AmsterdamMATH
3.
Zurück zum Zitat Shimizu N, Zhang W (1999) Fractional calculus approach to dynamic problems of viscoelastic materials. JSME Int J Ser C Mech Syst Mach Elem Mach Elem Manuf 42:825–837 Shimizu N, Zhang W (1999) Fractional calculus approach to dynamic problems of viscoelastic materials. JSME Int J Ser C Mech Syst Mach Elem Mach Elem Manuf 42:825–837
5.
Zurück zum Zitat Hilfer R (2000) Applications of fractional calculus in physics. World Scientific, SingaporeMATHCrossRef Hilfer R (2000) Applications of fractional calculus in physics. World Scientific, SingaporeMATHCrossRef
6.
Zurück zum Zitat Metzler R, Klafter J (2000) The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 339(1):1–77MathSciNetMATHCrossRef Metzler R, Klafter J (2000) The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 339(1):1–77MathSciNetMATHCrossRef
7.
8.
9.
Zurück zum Zitat Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput Math Appl 59(5):1810–1821MathSciNetMATHCrossRef Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput Math Appl 59(5):1810–1821MathSciNetMATHCrossRef
10.
Zurück zum Zitat Liu S, Wu X, Zhang YJ, Yang R (2017) Asymptotical stability of Riemann–Liouville fractional neutral systems. Appl Math Lett 86(1):65–71MathSciNetMATH Liu S, Wu X, Zhang YJ, Yang R (2017) Asymptotical stability of Riemann–Liouville fractional neutral systems. Appl Math Lett 86(1):65–71MathSciNetMATH
11.
Zurück zum Zitat Duarte-Mermoud MA, Aguila-Camacho N, Gallegos JA, Castro-Linares R (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numer Simul 22(1–3):650–659MathSciNetMATHCrossRef Duarte-Mermoud MA, Aguila-Camacho N, Gallegos JA, Castro-Linares R (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numer Simul 22(1–3):650–659MathSciNetMATHCrossRef
12.
Zurück zum Zitat Li HL, Jiang YL, Wang ZL, Zhang L, Teng ZD (2015) Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network. Appl Math Comput 270:269–277MathSciNetMATH Li HL, Jiang YL, Wang ZL, Zhang L, Teng ZD (2015) Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network. Appl Math Comput 270:269–277MathSciNetMATH
13.
Zurück zum Zitat Wu AL, Zeng ZG, Song XG (2016) Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing 177:489–496CrossRef Wu AL, Zeng ZG, Song XG (2016) Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing 177:489–496CrossRef
14.
Zurück zum Zitat Li XD, Zhang XI, Song SJ (2017) Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76:378–382MathSciNetMATHCrossRef Li XD, Zhang XI, Song SJ (2017) Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76:378–382MathSciNetMATHCrossRef
15.
Zurück zum Zitat Liu S, Li XY, Jiang W, Zhou XF (2012) Mittag–Leffler stability of nonlinear fractional neutral singular systems. Commun Nonlinear Sci Numer Simul 17(10):3961–3966MathSciNetMATHCrossRef Liu S, Li XY, Jiang W, Zhou XF (2012) Mittag–Leffler stability of nonlinear fractional neutral singular systems. Commun Nonlinear Sci Numer Simul 17(10):3961–3966MathSciNetMATHCrossRef
16.
Zurück zum Zitat Jia RW (2017) Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays. Fuzzy Set Syst 319:70–80MathSciNetMATHCrossRef Jia RW (2017) Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays. Fuzzy Set Syst 319:70–80MathSciNetMATHCrossRef
17.
Zurück zum Zitat Aouiti C, M’Hamdi MS, Cao JD, Alsaedi A (2017) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648CrossRef Aouiti C, M’Hamdi MS, Cao JD, Alsaedi A (2017) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648CrossRef
18.
Zurück zum Zitat Wang ZS, Liu L, Shan QH, Zhang HG (2017) Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Trans Neural Netw Learn Syst 26(10):2589–2595MathSciNetCrossRef Wang ZS, Liu L, Shan QH, Zhang HG (2017) Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Trans Neural Netw Learn Syst 26(10):2589–2595MathSciNetCrossRef
19.
Zurück zum Zitat Gong WQ, Liang JL, Cao JD (2015) Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw 70:81–89MATHCrossRef Gong WQ, Liang JL, Cao JD (2015) Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw 70:81–89MATHCrossRef
20.
Zurück zum Zitat Xiong WJ, Shi YB, Cao JD (2017) Stability analysis of two-dimensional neutral-type Cohen–Grossberg BAM neural networks. Neural Comput Appl 28(4):703–716CrossRef Xiong WJ, Shi YB, Cao JD (2017) Stability analysis of two-dimensional neutral-type Cohen–Grossberg BAM neural networks. Neural Comput Appl 28(4):703–716CrossRef
21.
Zurück zum Zitat Wang F, Yang YQ, Xu XY, Li L (2017) Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay. Neural Comput Appl 28(2):345–352CrossRef Wang F, Yang YQ, Xu XY, Li L (2017) Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay. Neural Comput Appl 28(2):345–352CrossRef
22.
Zurück zum Zitat Song QK, Yan H, Zhao ZJ, Liu YR (2016) Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neural Netw 79:108–116MATHCrossRef Song QK, Yan H, Zhao ZJ, Liu YR (2016) Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neural Netw 79:108–116MATHCrossRef
23.
Zurück zum Zitat Gong WQ, Liang JL, Zhang CJ, Cao JD (2016) Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process Lett 44(2):539–554CrossRef Gong WQ, Liang JL, Zhang CJ, Cao JD (2016) Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process Lett 44(2):539–554CrossRef
24.
Zurück zum Zitat Song QK, Shu HQ, Zhao ZJ, Liu YR, Alsaadie FE (2017) Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244:33–41CrossRef Song QK, Shu HQ, Zhao ZJ, Liu YR, Alsaadie FE (2017) Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244:33–41CrossRef
25.
Zurück zum Zitat Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26(23):4947–4960CrossRef Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26(23):4947–4960CrossRef
26.
Zurück zum Zitat Song C, Cao JD (2014) Dynamics in fractional-order neural networks. Neurocomputing 142:494–498CrossRef Song C, Cao JD (2014) Dynamics in fractional-order neural networks. Neurocomputing 142:494–498CrossRef
28.
Zurück zum Zitat Ding XS, Cao JD, Zhao X, Alsaadi FE (2017) Finite-time stability of fractional-order complex-valued neural networks with time delays. Neural Process Lett 46(2):561–580CrossRef Ding XS, Cao JD, Zhao X, Alsaadi FE (2017) Finite-time stability of fractional-order complex-valued neural networks with time delays. Neural Process Lett 46(2):561–580CrossRef
29.
Zurück zum Zitat Li RX, Cao JD, Alsaedi A, Alsaadi FE (2017) Stability analysis of fractional-order delayed neural networks. Nonlinear Anal Model Control 22(4):505–520MathSciNetMATHCrossRef Li RX, Cao JD, Alsaedi A, Alsaadi FE (2017) Stability analysis of fractional-order delayed neural networks. Nonlinear Anal Model Control 22(4):505–520MathSciNetMATHCrossRef
30.
Zurück zum Zitat Zhang H, Ye RY, Cao JD, Alsaedi A (2017) Existence and globally asymptotic stability of equilibrium solution for fractional-order hybrid BAM neural networks with distributed delays and impulses. Complexity 2017:1–13MathSciNetMATH Zhang H, Ye RY, Cao JD, Alsaedi A (2017) Existence and globally asymptotic stability of equilibrium solution for fractional-order hybrid BAM neural networks with distributed delays and impulses. Complexity 2017:1–13MathSciNetMATH
31.
Zurück zum Zitat Zhang H, Ye RY, Liu S, Cao JD, Alsaedi A, Li XD (2018) LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int J Syst Sci 49(3):537–545MathSciNetMATHCrossRef Zhang H, Ye RY, Liu S, Cao JD, Alsaedi A, Li XD (2018) LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int J Syst Sci 49(3):537–545MathSciNetMATHCrossRef
32.
Zurück zum Zitat Stamova I (2014) Global Mittag–Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dyn 77(4):1251–1260MathSciNetMATHCrossRef Stamova I (2014) Global Mittag–Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dyn 77(4):1251–1260MathSciNetMATHCrossRef
33.
Zurück zum Zitat Yang XS, Cao JD, Liang JL (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28(8):1878–1888MathSciNetCrossRef Yang XS, Cao JD, Liang JL (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28(8):1878–1888MathSciNetCrossRef
35.
Zurück zum Zitat Wu EL, Yang XS (2016) Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn 84(1):261–269MathSciNetMATHCrossRef Wu EL, Yang XS (2016) Adaptive synchronization of coupled nonidentical chaotic systems with complex variables and stochastic perturbations. Nonlinear Dyn 84(1):261–269MathSciNetMATHCrossRef
36.
Zurück zum Zitat Wu YY, Cao JD, Li QB, Alsaedi A, Alsaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139CrossRef Wu YY, Cao JD, Li QB, Alsaedi A, Alsaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139CrossRef
37.
Zurück zum Zitat Zhou C, Zhang WL, Yang XS, Xu C, Feng JW (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46(1):271–291CrossRef Zhou C, Zhang WL, Yang XS, Xu C, Feng JW (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46(1):271–291CrossRef
38.
Zurück zum Zitat Yang XS, Lam J, Ho DWC, Feng ZG (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Automat Control 62(11):5511–5521MathSciNetMATHCrossRef Yang XS, Lam J, Ho DWC, Feng ZG (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Automat Control 62(11):5511–5521MathSciNetMATHCrossRef
39.
Zurück zum Zitat Hu AH, Cao JD, Hu MF, Guo LX (2016) Distributed control of cluster synchronisation in networks with randomly occurring non-linearities. Int J Syst Sci 47(11):2588–2597MathSciNetMATHCrossRef Hu AH, Cao JD, Hu MF, Guo LX (2016) Distributed control of cluster synchronisation in networks with randomly occurring non-linearities. Int J Syst Sci 47(11):2588–2597MathSciNetMATHCrossRef
40.
Zurück zum Zitat He WL, Qian F, Cao JD (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Netw 85:1–9CrossRef He WL, Qian F, Cao JD (2017) Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control. Neural Netw 85:1–9CrossRef
41.
Zurück zum Zitat Xiong WJ, Zhang D, Cao JD (2017) Impulsive synchronisation of singular hybrid coupled networks with time-varying nonlinear perturbation. Int J Syst Sci 48(2):417–424MathSciNetMATHCrossRef Xiong WJ, Zhang D, Cao JD (2017) Impulsive synchronisation of singular hybrid coupled networks with time-varying nonlinear perturbation. Int J Syst Sci 48(2):417–424MathSciNetMATHCrossRef
42.
Zurück zum Zitat Chen JJ, Zeng ZG, Jiang P (2014) Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8MATHCrossRef Chen JJ, Zeng ZG, Jiang P (2014) Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8MATHCrossRef
43.
Zurück zum Zitat Ding ZX, Shen Y (2016) Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neural Netw 76:97–105MATHCrossRef Ding ZX, Shen Y (2016) Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neural Netw 76:97–105MATHCrossRef
44.
Zurück zum Zitat Wu HQ, Wang LF, Niu PF, Wang Y (2017) Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 235:264–273CrossRef Wu HQ, Wang LF, Niu PF, Wang Y (2017) Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 235:264–273CrossRef
45.
Zurück zum Zitat Zheng MW, Li LX, Peng HP, Xiao JH, Yang YX, Zhao H (2017) Finite-time projective synchronization of memristor-based delay fractional-order neural networks. Nonlinear Dyn 89(4):2641–2655MathSciNetMATHCrossRef Zheng MW, Li LX, Peng HP, Xiao JH, Yang YX, Zhao H (2017) Finite-time projective synchronization of memristor-based delay fractional-order neural networks. Nonlinear Dyn 89(4):2641–2655MathSciNetMATHCrossRef
46.
Zurück zum Zitat Bao HB, Park JH, Cao JD (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetMATHCrossRef Bao HB, Park JH, Cao JD (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetMATHCrossRef
47.
Zurück zum Zitat Rajivganthi C, Rihan FA, Lakshmanan S, Rakkiyappan R, Muthukumar P (2016) Synchronization of memristor-based delayed BAM neural networks with fractional-order derivatives. Complexity 21:412–426MathSciNetCrossRef Rajivganthi C, Rihan FA, Lakshmanan S, Rakkiyappan R, Muthukumar P (2016) Synchronization of memristor-based delayed BAM neural networks with fractional-order derivatives. Complexity 21:412–426MathSciNetCrossRef
48.
Zurück zum Zitat Wang F, Yang YQ, Hu MF, Xu XY (2015) Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. Phys A 434:134–143MathSciNetMATHCrossRef Wang F, Yang YQ, Hu MF, Xu XY (2015) Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. Phys A 434:134–143MathSciNetMATHCrossRef
49.
Zurück zum Zitat Bao HB, Park JH, Cao JD (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28MATHCrossRef Bao HB, Park JH, Cao JD (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28MATHCrossRef
50.
Zurück zum Zitat Gu YJ, Yu YG, Wang H (2016) Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty. J Frankl Inst 353(15):3657–3684MathSciNetMATHCrossRef Gu YJ, Yu YG, Wang H (2016) Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty. J Frankl Inst 353(15):3657–3684MathSciNetMATHCrossRef
51.
Zurück zum Zitat Yan JR, Shen JH (1999) Impulsive stabilization of impulsive functional differential equations by Lyapunov–Razumikhin functions. Nonlinear Anal Theory Methods Appl 37(2):245–255MathSciNetMATHCrossRef Yan JR, Shen JH (1999) Impulsive stabilization of impulsive functional differential equations by Lyapunov–Razumikhin functions. Nonlinear Anal Theory Methods Appl 37(2):245–255MathSciNetMATHCrossRef
52.
Zurück zum Zitat Bhalekar S, Daftardar-Gejji V (2011) Apredictor–corrector scheme for solving nonlinear delay differential equations of fractional order. J Fract Calc Appl 1(5):1–9 Bhalekar S, Daftardar-Gejji V (2011) Apredictor–corrector scheme for solving nonlinear delay differential equations of fractional order. J Fract Calc Appl 1(5):1–9
Metadaten
Titel
Global Mittag-Leffler Synchronization for Fractional-Order BAM Neural Networks with Impulses and Multiple Variable Delays via Delayed-Feedback Control Strategy
verfasst von
Renyu Ye
Xinsheng Liu
Hai Zhang
Jinde Cao
Publikationsdatum
10.02.2018
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 1/2019
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-018-9801-0

Weitere Artikel der Ausgabe 1/2019

Neural Processing Letters 1/2019 Zur Ausgabe

Neuer Inhalt