nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

02.12.2021 | Original Research

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

verfasst von: Yuhong Cheng, Hai Zhang, Weiwei Zhang, Hongmei Zhang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 5/2022

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

This paper focuses on the global Mittag–Leffler (M–L) synchronization for fractional-order inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M–L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

Vorheriger Artikel An approximation solution of linear Fredholm integro-differential equation using Collocation and Kantorovich methods

Nächster Artikel A novel approach for solving multi-term time fractional Volterra–Fredholm partial integro-differential equations

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)MATH

Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)MATH

Loghman, E., Bakhtiari-Nejad, F., Kamali, E.A., Abbaszadeh, M., Amabili, M.: Nonlinear vibration of fractional viscoelastic micro-beams. Int. J. Non Linear Mech. 137, 103811 (2021). https://doi.org/10.1016/j.ijnonlinmec.2021.103811CrossRefMATH

Tarasov, V.E.: Fractional econophysics: market price dynamics with memory effects. Physica A 557, 124865 (2020). https://doi.org/10.1016/j.physa.2020.124865MathSciNetCrossRefMATH

Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific Press, Singapore (2000)CrossRef

Yan, X., Zhang, Y., Wei, T.: Identify the fractional order and diffusion coefficient in a fractional diffusion wave equation. Comput. Appl. Math. 393, 113497 (2021). https://doi.org/10.1016/j.cam.2021.113497MathSciNetCrossRefMATH

Baleanu, D., Machado, J.A.T., Luo, A.C.J.: Fractional Dynamics and Control. Springer, New York (2012)CrossRef

Al-NassirM, S.: Dynamic analysis of a harvested fractional-order biological system with its discretization. Chaos Solitons Fract. 152, 111308 (2021). https://doi.org/10.1016/j.chaos.2021.111308MathSciNetCrossRefMATH

Syed Ali, M., Narayanan, G., Saroha, S., Priya, B., Thakur, G.K.: Finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks with time delay and leakage term. Math. Comput. Simul. 185, 468–485 (2021). https://doi.org/10.1016/j.matcom.2020.12.035MathSciNetCrossRefMATH

10.

Yang, Z., Zhang, J., Niu, Y.: Finite-time stability of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. Appl. Math. Comput. 63, 501–522 (2020). https://doi.org/10.1007/s12190-020-01327-6MathSciNetCrossRefMATH

11.

Ma, K., Sun, S.: Finite-time stability of linear fractional time-delay \(q\)-difference dynamical system. Appl. Math. Comput. 57, 591–604 (2018). https://doi.org/10.1007/s12190-017-1123-2MathSciNetCrossRefMATH

12.

Syed Ali, M., Narayanan, G., Shekher, V., Alsaedi, A., Ahmad, B.: Global Mittag–Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays. Commun. Nonlinear Sci. Numer. Simul. 183, 105088 (2020). https://doi.org/10.1016/j.cnsns.2019.105088MathSciNetCrossRefMATH

13.

Ke, L.: Mittag–Leffler stability and asymptotic \(\omega \)-periodicity of fractional-order inertial neural networks with time-delays. Neurocomputing 465, 53–62 (2021). https://doi.org/10.1016/j.neucom.2021.08.121CrossRef

14.

Sriraman, R., Cao, Y., Samidurai, R.: Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays. Math. Comput. Simul. 171, 103–118 (2020). https://doi.org/10.1016/j.matcom.2019.04.001MathSciNetCrossRefMATH

15.

Gu, Y., Wang, H., Yu, Y.: Stability and synchronization for Riemann–Liouville fractional-order time-delayed inertial neural networks. Neurocomputing 340, 270–280 (2019). https://doi.org/10.1016/j.neucom.2019.03.005CrossRef

16.

Pahnehkolaei, S.M.A., Alfi, A., Tenreiro Machado, J.A.: Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition. Appl. Math. Comput. 359, 278–293 (2019). https://doi.org/10.1016/j.amc.2019.04.083

17.

Li, H., Kao, Y., Hu, C., Jiang, H., Jiang, Y.: Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects. Chaos Solitons Fract. 143, 110598 (2021). https://doi.org/10.1016/j.chaos.2020.110598MathSciNetCrossRefMATH

18.

Wei, X., Zhang, Z., Lin, C., Chen, J.: Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays. Appl. Math. Comput. 403, 126194 (2021). https://doi.org/10.1016/j.amc.2021.126194MathSciNetCrossRefMATH

19.

Miao, P., Shen, Y., Li, Y., Bao, L.: Finite-time recurrent neural networks for solving nonlinear optimization problems and their application. Neurocomputing 177, 120–129 (2016). https://doi.org/10.1016/j.neucom.2015.11.014CrossRef

20.

Rakkiyappan, R., Li, X., O’Regan, D.: Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays. J. Appl. Math. Comput. 40, 289–317 (2012). https://doi.org/10.1007/s12190-012-0554-z

21.

Liu, W., Huang, J., Yao, Q.: Stability analysis for quaternion-valued inertial memristor-based neural networks with time delays. Neurocomputing 448, 67–81 (2021). https://doi.org/10.1016/j.neucom.2021.03.106CrossRef

22.

Wei, F., Chen, G., Wang, W.: Finite-time stabilization of memristor-based inertial neural networks with time-varying delays combined with interval matrix method. Knowl. Based Syst. 230, 107395 (2021). https://doi.org/10.1016/j.knosys.2021.107395CrossRef

23.

Tang, Q., Jian, J.: Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays. Math. Comput. Simul. 159, 39–56 (2019). https://doi.org/10.1016/j.matcom.2018.10.009MathSciNetCrossRefMATH

24.

Qiu, J., Yang, X., Cao, J.: Pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Net. Off. J. Int. Neural Netw. Soc. 65, 80–91 (2015). https://doi.org/10.1016/j.neunet.2015.01.008

25.

Feng, Y., Yang, X., Qiang, S., Cao, J.: Synchronization of memristive neural networks with mixed delays via quantized intermittent control. Appl. Math. Comput. 339, 874–887 (2018). https://doi.org/10.1016/j.amc.2018.08.009MathSciNetCrossRefMATH

26.

Babcock, K.L., Westervelt, R.M.: Stability and dynamics of simple electronic neural networks with added inertia. Physica D 23, 464–469 (1986). https://doi.org/10.1016/0167-2789(86)90152-1CrossRef

27.

Stamova, I.: Global Mittag–Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dyn. 77, 1251–1260 (2014). https://doi.org/10.1007/s11071-014-1375-4MathSciNetCrossRefMATH

28.

Vadivel, R., Hammachukiattikul, P., Rajchakit, G., Syed, Ali M., Unyong, B.: Finite-time event-triggered approach for recurrent neural networks with leakage term and its application. Math. Comput. Simul. 182, 765–790 (2021). https://doi.org/10.1016/j.matcom.2020.12.001

29.

Li, H., Jiang, H., Cao, J.: Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays. Neurocomputing 385, 211–219 (2020). https://doi.org/10.1016/j.neucom.2019.12.018CrossRef

30.

Zhang, H., Cheng, J., Zhang, H.M., Zhang, W., Cao, J.: Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays. Chaos Solitons Fract. 152, 111432 (2021). https://doi.org/10.1016/j.chaos.2021.111432MathSciNetCrossRefMATH

31.

Du, F., Lu, J.: New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays. Chaos Solitons Fract. 151, 111225 (2021). https://doi.org/10.1016/j.chaos.2021.111225MathSciNetCrossRefMATH

32.

Zhang, Y., Liu, S., Yang, R., Tan, Y., Li, X.: Global synchronization of fractional coupled networks with discrete and distributed delays. Physica A 514, 830–837 (2019). https://doi.org/10.1016/j.physa.2018.09.129MathSciNetCrossRefMATH

33.

Wang, C., Zhang, H., Zhang, H.M., Zhang, W.: Globally projective synchronization for Caputo fractional quaternion-valued neural networks with discrete and distributed delays. AIMS Math. 6(12), 14000–14012 (2021). https://doi.org/10.3934/math.2021809MathSciNetCrossRefMATH

34.

Zhang, L., Zhong, J., Lu, J.: Intermittent control for finite-time synchronization of fractional-order complex networks. Neural Netw. 144, 11–20 (2021). https://doi.org/10.1016/j.neunet.2021.08.004CrossRef

35.

Li, L., Liu, X., Tang, M., Zhang, S.: Asymptotical synchronization analysis of fractional-order complex neural networks with non-delayed and delayed couplings. Neural Netw. 445, 180–193 (2021). https://doi.org/10.1016/j.neucom.2021.03.001CrossRef

36.

Syed Ali, M., Hymavathi, M., Senan, S., Shekher, V., Arik, S.: Global asymptotic synchronization of impulsive fractional-order complex-valued memristor-based neural networks with time varying delays. Commun. Nonlinear Sci. Numer. Simul. 78, 104869 (2019). https://doi.org/10.1016/j.cnsns.2019.104869MathSciNetCrossRefMATH

37.

Hu, T., Zhang, X., Zhong, S.: Global asymptotic synchronization of nonidentical fractional-order neural networks. Neurocomputing 313, 39–46 (2018). https://doi.org/10.1016/j.neucom.2018.05.098CrossRef

38.

Ye, R., Liu, X., Zhang, H., Cao, J.: Global Mittag–Leffler synchronization for fractional-order BAM neural networks with impulses and multiple variable delays via delayed-feedback control strategy. Neural Process. Lett. 49, 1–18 (2019). https://doi.org/10.1007/s11063-018-9801-0CrossRef

39.

Pratap, A., Raja, R., Sowmiya, C., Bagdasar, O., Cao, J., Rajchakit, G.: Robust generalized Mittag–Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Process. Lett. 103, 128–141 (2018). https://doi.org/10.1016/j.neunet.2018.03.012CrossRefMATH

40.

Chen, J., Li, C., Yang, X.: Global Mittag–Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomputing 313, 324–332 (2018). https://doi.org/10.1016/j.neucom.2018.06.029CrossRef

41.

Xiao, J., Zhong, S., Wen, S.: Improved approach to the problem of the global Mittag–Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities. Neural Netw. 133, 87–100 (2021). https://doi.org/10.1016/j.neunet.2020.10.008CrossRefMATH

42.

Zhang, W., Sha, C., Cao, J., Wang, G., Wang, Y.: Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field. Appl. Math. Comput. 400, 126045 (2021). https://doi.org/10.1016/j.amc.2021.126045MathSciNetCrossRefMATH

43.

Yang, S., Hu, C., Yu, J., Jiang, H.: Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order. Chaos Solitons Fract. 147, 110911 (2021). https://doi.org/10.1016/j.chaos.2021.110911MathSciNetCrossRefMATH

44.

Chen, J., Zeng, Z., Jiang, P.: Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw. 51, 1–8 (2014). https://doi.org/10.1016/j.neunet.2013.11.016CrossRefMATH

45.

Li, H., Hu, C., Zhang, L., Jiang, H., Cao, J.: Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks. Appl. Math. Comput. 409, 126377 (2021). https://doi.org/10.1016/j.amc.2021.126377MathSciNetCrossRefMATH

46.

Tang, R., Su, H., Zou, Y., Yang, X.: Finite-time synchronization of Markovian coupled neural networks with delays via intermittent quantized control: linear programming approach. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3069926

47.

Yang, X., Li, X., Lu, J., Cheng, Z.: Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control. Neurocomputing 50, 4043–4052 (2020). https://doi.org/10.1109/TCYB.2019.2938217CrossRef

48.

Yang, X., Li, X., Lu, J., Rutkowski, L.: Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching. Neurocomputing 31, 5483–5496 (2020). https://doi.org/10.1109/TNNLS.2020.2968342MathSciNetCrossRef

49.

Yang, X., Feng, Z., Feng, J., Cao, J.: Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw. 85, 157–164 (2017). https://doi.org/10.1016/j.neunet.2016.10.006CrossRefMATH

50.

Yang, X., Lu, J., Ho, D., Song, Q.: Synchronization of uncertain hybrid switching and impulsive complex networks. Appl. Math. Model. 59, 379–392 (2018). https://doi.org/10.1016/j.apm.2018.01.046MathSciNetCrossRefMATH

51.

Yang, X., Wan, X., Cheng, Z., Cao, J., Rutkowski, L.: Synchronization of switched discrete-time neural networks via quantized output control with actuator fault. IEEE Trans. Neural Netw. Learn. Syst. 32, 4191–4201 (2021). https://doi.org/10.1109/TNNLS.2020.3017171MathSciNetCrossRef

52.

Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Castro-Linares, R.: Using general quadratic Lyapunov functions to prove Lyapunovuniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 22, 650–659 (2015). https://doi.org/10.1016/j.cnsns.2014.10.008MathSciNetCrossRefMATH

Titel: Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay
verfasst von: Yuhong Cheng
Hai Zhang
Weiwei Zhang
Hongmei Zhang
Publikationsdatum: 02.12.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 5/2022
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01672-0

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 5/2022

Iterative oscillation criteria for first-order difference equations with non-monotone advanced arguments

Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model

Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation

On the behavior of the solutions of an abstract system of difference equations

Energy of interval-valued fuzzy graphs and its application in ecological systems

Multi-inertial parallel hybrid projection algorithm for generalized split null point problems

Premium Partner