Synchronization of fractional chaotic complex networks with delays

Jian-Bing Hu; Hua Wei; Ye-Feng Feng; Xiao-Bo Yang

Kybernetika (2019)

  • Volume: 55, Issue: 1, page 203-215
  • ISSN: 0023-5954

Abstract

top
The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function V and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.

How to cite

top

Hu, Jian-Bing, et al. "Synchronization of fractional chaotic complex networks with delays." Kybernetika 55.1 (2019): 203-215. <http://eudml.org/doc/294163>.

@article{Hu2019,
abstract = {The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function $V$ and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.},
author = {Hu, Jian-Bing, Wei, Hua, Feng, Ye-Feng, Yang, Xiao-Bo},
journal = {Kybernetika},
keywords = {fractional complex networks; delays; Lyapunov-Krasovskii theorem; synchronization},
language = {eng},
number = {1},
pages = {203-215},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Synchronization of fractional chaotic complex networks with delays},
url = {http://eudml.org/doc/294163},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Hu, Jian-Bing
AU - Wei, Hua
AU - Feng, Ye-Feng
AU - Yang, Xiao-Bo
TI - Synchronization of fractional chaotic complex networks with delays
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 203
EP - 215
AB - The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function $V$ and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.
LA - eng
KW - fractional complex networks; delays; Lyapunov-Krasovskii theorem; synchronization
UR - http://eudml.org/doc/294163
ER -

References

top
  1. Ahmad, B., Ntouyas, S. K., Tariboon, J., Alsaedi, A., Alsulami, H. H., 10.1016/j.amc.2016.01.051, Appl. Math. Comput. 281 (2016), 199-213. MR3466095DOI10.1016/j.amc.2016.01.051
  2. An, F., Gao, X. Y., Guan, J. H., Li, H. J., Liu, Q., 10.1016/j.physa.2015.12.050, Physica A: Statist. Mechanics and Its Appl. 447 (2016), 276-285. DOI10.1016/j.physa.2015.12.050
  3. Aguila-Camacho, N., Duarte-Mermoud, M. A., Gallegos, J. A., 10.1016/j.cnsns.2014.01.022, Commu. Nonlinear Science Numer. Simul. 19 (2014), 2951-2957. MR3182869DOI10.1016/j.cnsns.2014.01.022
  4. Baleanu, D., Ranjbar, A., Sadati, S. J., Delavari, R. H., Abdeljawad, T., Gejji, V., Lyapunov-Krasovskii stability theorem for fractional systems with delay., Romanian J. Phys. 56 (2011), 636-643. MR2821032
  5. Chen, Y., Lü, J., 10.1016/j.automatica.2017.07.059, Automatica 85 (2017), 356-361. MR3712878DOI10.1016/j.automatica.2017.07.059
  6. Chen, L. P., Pan, W., Wu, R. C., Machado, J. A. T., Lopes, A. M., 10.1063/1.4958717, Chaos 26 (2016), 8, 084303. MR3522604DOI10.1063/1.4958717
  7. Dai, H., Si, G. Q., Jia, L. X., Zhang, Y. B., 10.1088/0031-8949/88/05/055006, Physica Scripta 88 (2013), 5, 055006. DOI10.1088/0031-8949/88/05/055006
  8. David, S. A., Machado, J. A. T., Quintino, D. D., Balthazar, J. M., 10.1016/j.matcom.2015.11.004, Math. Computers Simul. 122 (2016), 55-68. MR3436941DOI10.1016/j.matcom.2015.11.004
  9. Hu, J. B., Lu, G. P., Zhao, L. D., 10.1007/s11071-015-2390-9, Nonlinear dynamics 83 (2016), 1101-1108. MR3435929DOI10.1007/s11071-015-2390-9
  10. Hu, J. B., Wei, H., Zhao, L. D., 10.14736/kyb-2015-6-1068, Kybernetika 51 (2015), 1068-1083. MR3453686DOI10.14736/kyb-2015-6-1068
  11. Li, B. C., 10.1016/j.apm.2015.09.092, Appl. Math. Modell. 40 (2016), 2983-2998. MR3454505DOI10.1016/j.apm.2015.09.092
  12. Li, Y., Wu, X., Lu, J. A., Lü, J., 10.1109/tcsii.2015.2468924, IEEE Trans. Circuits Systems II Express Briefs 63 (2016), 206-210. DOI10.1109/tcsii.2015.2468924
  13. Liang, S., Wu, R. C., Chen, L. P., 10.1016/j.physa.2015.10.011, Physica a-Statistical Mechanics and Its Applications 444(2016), 49-62. MR3428092DOI10.1016/j.physa.2015.10.011
  14. Liu, K., Wu, L., Lü, J., Zhu, H., 10.1007/s11431-015-5989-7, Science China Technol. Sci. 59 (2016), 22-32. DOI10.1007/s11431-015-5989-7
  15. Liu, K., Zhu, H., Lü, J., 10.1109/tcsi.2017.2675922, IEEE Trans. Circuits Systems I Regular Papers 64(2017), 1891-1902. MR3671833DOI10.1109/tcsi.2017.2675922
  16. Rivero, M., Rogosin, S. V., Machado, J. A. T., Trujillo, J. J., Stability of fractional order systems., Math. Problems Engrg. 2013 (2013), 1-14. MR3062648
  17. Spasic, D. T., Kovincic, N. I., Dankuc, D. V., 10.1016/j.cnsns.2016.01.004, Comm. Nonlinear Sci. Numer. Simul. 37 (2016), 193-199. MR3466784DOI10.1016/j.cnsns.2016.01.004
  18. Tang, H. W., Chen, L., Lu, J. A., Tse, C. K., 10.1016/j.physa.2008.05.047, Physica a-Statistical Mechanics and Its Applications 387 (2008) 5623-5630. DOI10.1016/j.physa.2008.05.047
  19. Tang, Y., Gao, H. J., Kurths, J., 10.1109/tcsi.2013.2285699, IEEE Trans. Circuits Systems I-Regular Papers, 61 (2014), 1508-1519. MR3200565DOI10.1109/tcsi.2013.2285699
  20. Uncini, A., Piazza, F., 10.1109/tnn.2003.809411, IEEE Trans. Neural Networks 14 (2003), 399-412. DOI10.1109/tnn.2003.809411
  21. Wang, Y., Li, T. Z., 10.1016/j.physa.2015.02.051, Physica a-Statistical Mechanics and Its Applications 428 (2015), 1-12. MR3322873DOI10.1016/j.physa.2015.02.051
  22. Wang, J. W., Ma, Q. H., Chen, A. M., Liang, Z. P., 10.1016/j.isatra.2015.02.002, ISA Trans. 57 (2015), 111-116. DOI10.1016/j.isatra.2015.02.002
  23. Wang, F., Yang, Y. Q., Hu, A. H., Xu, X. Y., 10.1007/s11071-015-2292-x, Nonlinear Dynamics 82 (2015), 1979-1987. MR3422995DOI10.1007/s11071-015-2292-x
  24. Wang, Z., Huang, X., Li, Y. X., Song, X. N., 10.1088/1674-1056/22/1/010504, Chinese Physics B 22 (2013), 1, 010504. DOI10.1088/1674-1056/22/1/010504
  25. Wang, F., Yang, Y. Q., Hu, M. F., Xu, X. Y., 10.1016/j.physa.2015.03.089, Physica a-Statistical Mechanics and Its Applications 434 (2015), 134-143. MR3349715DOI10.1016/j.physa.2015.03.089
  26. Wu, G. C., Baleanu, D., 10.1007/s11071-014-1250-3, Nonlinear Dynamics 80 (2015), 1697-1703. MR3343425DOI10.1007/s11071-014-1250-3
  27. Wu, G. C., Baleanu, D., Deng, Z. G., Zeng, S. D., 10.1016/j.physa.2015.06.024, Physica a-Statistical Mechanics and Its Applications 438 (2015), 335-339. MR3384291DOI10.1016/j.physa.2015.06.024
  28. Yi, J. W., Wang, Y. W., Xiao, J. W., Huang, Y. H., 10.1080/00207721.2014.919426, Int. J. Systems Sci. 47 (2016), 1221-1229. MR3441585DOI10.1080/00207721.2014.919426
  29. Zhang, W. B., Tang, Y., Miao, Q. Y., Fang, J. A., 10.1109/tnnls.2013.2294727, IEEE Trans. Neural Networks Learning Systems 25 (2014), 1758-1768. DOI10.1109/tnnls.2013.2294727
  30. Zhao, L. D., Hu, J. B., Fang, J. A., Cui, W. X., Xu, Y. L., Wang, X., 10.1016/j.isatra.2013.07.001, ISA Trans. 52 (2013),738-743. DOI10.1016/j.isatra.2013.07.001
  31. Zhou, W. N., Dai, A. D., Yang, J., Liu, H. S., Liu, X. L., 10.1007/s11071-014-1418-x, Nonlinear Dynamics 78(2014), 15-27. MR3266422DOI10.1007/s11071-014-1418-x
  32. Zhou, Y., Ionescu, C., Machado, J. A. T., 10.1007/s11071-015-2069-2, Nonlinear Dynamics 80 (2015), 1661-1664. MR3343421DOI10.1007/s11071-015-2069-2
  33. Zhou, J., Chen, J., Lu, J. A., Lü, J., 10.1109/tac.2016.2615679, IEEE Trans. Automat. Control 62 (2017), 3468-3473. MR3669467DOI10.1109/tac.2016.2615679

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.