IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v508y2018icp155-165.html
   My bibliography  Save this article

Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks

Author

Listed:
  • Zhang, Hai
  • Ye, Miaolin
  • Ye, Renyu
  • Cao, Jinde

Abstract

This paper focuses on discussing the synchronization stability problem of the Riemann–Liouville fractional coupled complex interconnected delayed neural networks. Several globally asymptotic stability criteria for considered network systems are established in terms of Lyapunov functional approach and linear matrix inequality technique. The relationships between the stability of fractional-order isolated neural networks and the synchronization of fractional-order coupled complex neural networks are discussed in detail. The main advantage is to avoid calculating the fractional derivative of Lyapunov functional to discuss the synchronization stability conditions. A numerical example is also performed to demonstrate the validity and feasibility of the proposed results.

Suggested Citation

  • Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    • Handle: RePEc:eee:phsmap:v:508:y:2018:i:c:p:155-165
    DOI: 10.1016/j.physa.2018.05.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118306046
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.05.060?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hai Zhang & Renyu Ye & Song Liu & Jinde Cao & Ahmad Alsaedi & Xiaodi Li, 2018. "LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 537-545, February.
    2. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    3. Fang, Qingxiang & Peng, Jigen, 2018. "Synchronization of fractional-order linear complex networks with directed coupling topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 542-553.
    4. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    5. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    6. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    7. Zhao, Yi & Fu, Fangfang & Wang, Jingyi & Feng, Jianwen & Zhang, Haiyu, 2018. "Synchronization of hybrid-coupled delayed dynamical networks with noises by partial mixed impulsive control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1181-1193.
    8. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    9. Liu, Xiwei & Chen, Tianping, 2008. "Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4429-4439.
    10. Cheng, Lin & Yang, Yongqing & Li, Li & Sui, Xin, 2018. "Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 273-286.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    2. Xu, Wei & Zhu, Song & Fang, Xiaoyu & Wang, Wei, 2019. "Adaptive anti-synchronization of memristor-based complex-valued neural networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Weiwei Zhang & Jinde Cao & Dingyuan Chen & Ahmed Alsaedi, 2019. "Out Lag Synchronization of Fractional Order Delayed Complex Networks with Coupling Delay via Pinning Control," Complexity, Hindawi, vol. 2019, pages 1-7, August.
    4. Wang, Li & Jia, Xiaoyu & Pan, Xiuyu & Xia, Chengyi, 2021. "Extension of synchronizability analysis based on vital factors: Extending validity to multilayer fully coupled networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Zhang, Weiwei & Zhang, Hai & Cao, Jinde & Zhang, Hongmei & Chen, Dingyuan, 2020. "Synchronization of delayed fractional-order complex-valued neural networks with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    6. Zhang, Hai & Cheng, Jingshun & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2021. "Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Shi, Zhicheng & Yang, Yongqing & Chang, Qi & Xu, Xianyun, 2020. "The optimal state estimation for competitive neural network with time-varying delay using Local Search Algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Shuang Wang & Hai Zhang & Weiwei Zhang & Hongmei Zhang, 2021. "Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    9. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    10. Zhang, Hai & Cheng, Yuhong & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2022. "Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 341-357.
    11. Zonglun Li & Yuliya Tsybina & Susanna Gordleeva & Alexey Zaikin, 2022. "Impact of Astrocytic Coverage of Synapses on the Short-Term Memory of a Computational Neuron-Astrocyte Network," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    12. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Chuan & Wang, Xingyuan & Luo, Chao & Li, Junqiu & Wang, Chunpeng, 2018. "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 251-264.
    2. Du, Hongyue, 2011. "Function projective synchronization in drive–response dynamical networks with non-identical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 510-514.
    3. J. H. Park & S. M. Lee & H. Y. Jung, 2009. "LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 357-367, November.
    4. Wu, Jianshe & Jiao, Licheng, 2008. "Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2111-2119.
    5. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    6. Tseng, Jui-Pin, 2016. "A novel approach to synchronization of nonlinearly coupled network systems with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 266-280.
    7. Liu, Xiwei & Chen, Tianping, 2007. "Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 82-92.
    8. Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.
    9. Liu, Tao & Dimirovski, Georgi M. & Zhao, Jun, 2008. "Exponential synchronization of complex delayed dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 643-652.
    10. Hu, Binxin & Song, Qiankun & Zhao, Zhenjiang, 2020. "Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    11. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    12. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    13. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    14. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    15. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    16. Tri Tran & Q. P. Ha, 2014. "Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 933-950, June.
    17. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
    18. He, Guangming & Yang, Jingyu, 2008. "Adaptive synchronization in nonlinearly coupled dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1254-1259.
    19. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    20. Yang, Yong & Tu, Lilan & Li, Kuanyang & Guo, Tianjiao, 2019. "Optimized inter-structure for enhancing the synchronizability of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 310-318.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:508:y:2018:i:c:p:155-165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.