Skip to main content
SpringerLink
Log in

Passivity and Synchronization of Coupled Reaction–Diffusion Cohen–Grossberg Neural Networks with Fixed and Switching Topologies

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper investigates the passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs) with constant and delayed couplings respectively. On the one side, a CRDCGNNs model with fixed topology is introduced, and several sufficient conditions which ensure passivity and synchronization for this type of network are derived respectively by exploiting some inequality techniques and constructing appropriate Lyapunov functional. On the other side, considering that topology structure of a network may change by switches in some cases, we also concern on the passivity and synchronization of CRDCGNNs with switching topology. Finally, the correctness of the obtained passivity and synchronization criteria are corroborated by two illustrative examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Song Q, Cao JD, Liu F (2010) Synchronization of complex dynamical detworks with nonidentical nodes. Phys Lett A 374(4):544–551

    Article  MATH  Google Scholar 

  2. Lu JQ, Ho DWC, Cao JD (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7):1215–1221

    Article  MathSciNet  MATH  Google Scholar 

  3. Zheng ZW, Huang YT, Xie LH, Zhu B (2017) Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output. IEEE Trans Control Syst Technol. https://doi.org/10.1109/TCST.2017.2728518

    Article  Google Scholar 

  4. Lu JQ, Ho DWC (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern 40(2):350–361

    Article  Google Scholar 

  5. Lu JQ, Ho DWC, Wu LG (2009) Exponential stabilization of switched stochastic dynamical networks. Nonlinearity 22:889–911

    Article  MathSciNet  MATH  Google Scholar 

  6. Huang TW, Chen GR, Kurths J (2011) Synchronization of chaotic systems with time-varying coupling delays. Discrete Continuous Dyn Syst B 16(4):1071–1082

    Article  MathSciNet  MATH  Google Scholar 

  7. Li YY (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46(1):59–69

    Article  Google Scholar 

  8. Lu JQ, Wang ZD, Cao JD, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176

    Article  MATH  Google Scholar 

  9. Lu JQ, Ding CD, Lou JG, Cao JD (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Franklin Inst 352(11):5024–5041

    Article  MathSciNet  MATH  Google Scholar 

  10. Bevelevich V (1968) Classical network synthesis. Van Nostrand, New York

    Google Scholar 

  11. Liu YH, Liu YX, Huo HJ, Chu B, Li JY (2013) Passivity control of induction motors based on adaptive observer design. In: Proceedings of the 3rd IFAC conference intelligent control and automation sciences, vol 46, no. 20, pp 176–181

  12. Yang CY, Sun J, Zhang QL, Ma XP (2013) Lyapunov stability and strong passivity analysis for nonlinear descriptor systems. IEEE Trans Circuits Syst I Regul Pap 60(4):1003–1012

    Article  MathSciNet  Google Scholar 

  13. Ihle IAF, Arcak M, Fossen TI (2007) Passivity-based designs for synchronized path-following. Automatica 43(9):1508–1518

    Article  MathSciNet  MATH  Google Scholar 

  14. Zheng ZW, Sun L, Xie LH (2017) Error constrained LOS path following of a surface vessel with actuator saturation and faults. Syst IEEE Trans Syst Man Cybern. https://doi.org/10.1109/TSMC.2017.2717850

    Article  Google Scholar 

  15. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13(5):815–826

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Zheng CD, Shan QH, Zhang HG, Wang ZS (2013) On stabilization of stochastic Cohen–Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching. IEEE Trans Neural Netw Learn Syst 24(5):800–811

    Article  Google Scholar 

  18. Zhu QX, Cao JD (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21(8):1314–1325

    Article  Google Scholar 

  19. Hu L, Gao HB, Shi P (2009) New stability criteria for Cohen–Grossberg neural networks with time delays. IET Control Theory Appl 3(9):1275–1282

    Article  MathSciNet  Google Scholar 

  20. Chen TP, Rong LB (2004) Robust global exponential stability of Cohen–Grossberg neural networks with time delays. IEEE Trans Neural Netw 15(1):203–206

    Article  Google Scholar 

  21. Li ZH, Liu L, Zhu QX (2016) Mean-square exponential input-to-state stability of delayed Cohen–Grossberg neural networks with Markovian switching based on vector Lyapunov functions. Neural Netw 84:39–46

    Article  Google Scholar 

  22. Liu YR, Liu WB, Obaid MA, Abbas IA (2016) Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays. Neurocomputing 177:409–415

    Article  Google Scholar 

  23. Zhang ZQ, Yu SH (2016) Global asymptotic stability for a class of complex-valued Cohen–Grossberg neural networks with time delays. Neurocomputing 171:1158–1166

    Article  Google Scholar 

  24. Jian JG, Jiang WL (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhou WS, Teng LY, Xu DY (2015) Mean-square exponentially input-to-state stability of stochastic Cohen–Grossberg neural networks with time-varying delays. Neurocomputing 153:54–61

    Article  Google Scholar 

  26. Arunkumar A, Mathiyalagan K, Sakthivel R, Anthoni SM (2012) Robust passivity of fuzzy Cohen–Grossberg neural networks with time-varying delays. Mathematical modelling and scientific computing. Springer, Berlin, pp 263–270

    MATH  Google Scholar 

  27. Nagamani G, Radhika T (2016) A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time-varying delays. Math Methods Appl Sci 39(13):3880–3896

    Article  MathSciNet  MATH  Google Scholar 

  28. Ramasamy S, Nagamani G, Zhu QX (2016) Robust dissipativity and passivity analysis for discrete-time stochastic T–S fuzzy Cohen–Grossberg Markovian jump neural networks with mixed time delays. Nonlinear Dyn 85(4):2777–2799

    Article  MATH  Google Scholar 

  29. Zhang YT, Xue YM (2015) Global exponential stability of impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Poincarè inequality. Proceedings of the 34th Chinese control conference, pp 1624–1629

  30. Wang ZS, Zhang HG, Li P (2010) An LMI approach to stability analysis of reaction–diffusion Cohen–Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays. IEEE Trans Syst Man Cybern 40(6):1596–1606

    Article  Google Scholar 

  31. Wei TD, Wang LS, Wang YF (2017) Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and wiener processes. Neurocomputing 239:19–27

    Article  Google Scholar 

  32. Shi YC, Zhu PY (2014) Asymptotic stability analysis of stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed time delays. Appl Math Comput 242:159–167

    MathSciNet  MATH  Google Scholar 

  33. Wang JL, Wu HN, Guo L (2013) Stability analysis of reaction–diffusion Cohen–Grossberg neural networks under impulsive control. Neurocomputing 106:21–30

    Article  Google Scholar 

  34. Zhou CH, Zhang HY, Zhang HB, Dang CY (2012) Global exponential stability of impulsive fuzzy Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms. Neurocomputing 91:67–76

    Article  Google Scholar 

  35. Wang CH, Kao YG, Yang GW (2012) Exponential stability of impulsive stochastic fuzzy reaction–diffusion Cohen–Grossberg neural networks with mixed delays. Neurocomputing 89:55–63

    Article  Google Scholar 

  36. Zhu QX, Cao JD (2011) Exponential stability analysis of stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed delays. Neurocomputing 74(17):3084–3091

    Article  Google Scholar 

  37. Li ZA, Li KL (2009) Stability analysis of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. Appl Math Model 33(3):1337–1348

    Article  MathSciNet  MATH  Google Scholar 

  38. Wan L, Zhou QH (2008) Exponential stability of stochastic reaction–diffusion Cohen–Grossberg neural networks with delays. Appl Math Comput 206(2):818–824

    MathSciNet  MATH  Google Scholar 

  39. Li RX, Cao JD, Alsaedi A, Ahmad B (2017) Passivity analysis of delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy-Poincarè inequality. J Franklin Inst 354(7):3021–3038

    Article  MathSciNet  MATH  Google Scholar 

  40. Chen WZ, Huang YL, Ren SY (2017) Passivity and robust passivity of delayed Cohen-Grossberg neural networks with and without reaction-diffusion terms. Circuits Syst Signal Process. https://doi.org/10.1007/s00034-017-0693-4

    Article  MATH  Google Scholar 

  41. Liang JL, Wang ZD, Liu YR, Liu XH (2008) Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Trans Neural Netw 19(11):1910–1921

    Article  Google Scholar 

  42. Liu XY, Cao JD, Yu WW, Song Q (2016) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern 46(10):2360–2371

    Article  Google Scholar 

  43. Wang HW, Song QK (2011) Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays. Neurocomputing 74(10):1572–1584

    Article  Google Scholar 

  44. Yu WW, Cao JD, Lu WL (2010) Synchronization control of switched linearly coupled neural networks with delay. Neurocomputing 73:858–866

    Article  Google Scholar 

  45. Zhang WB, Tang Y, Miao QY, Du W (2013) Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans Neural Netw Learn Syst 24(8):1316–1326

    Article  Google Scholar 

  46. Wang JL, Wu HN, Huang TW, Ren SY (2015) Passivity and synchronization of linearly coupled reaction-diffusion neural networks with adaptive coupling. IEEE Trans Syst Man Cybern 45(9):1942–1952

    Google Scholar 

  47. Wang JL, Wu HN, Huang TW, Ren SY, Wu JG (2017) Passivity analysis of coupled reaction–diffusion neural networks with Dirichlet boundary conditions. IEEE Trans Syst Man Cybern 47(8):2148–2159

    Article  Google Scholar 

  48. Zhang HT, Li T, Fei SM (2011) Synchronization for an array of coupled Cohen–Grossberg neural networks with time-varying delay. Math Probl Eng 4:903–908

    MathSciNet  MATH  Google Scholar 

  49. Liu QM, Xu R (2012) Synchronization between bidirectional coupled nonautonomous delayed Cohen–Grossberg neural networks. Abstr Appl Anal 2012:1–16

    MathSciNet  MATH  Google Scholar 

  50. Li T, Song AG, Fei SM (2010) Synchronization control for arrays of coupled discrete-time delayed Cohen–Grossberg neural networks. Neurocomputing 74(1–3):197–204

    Article  Google Scholar 

  51. Chen WZ, Huang YL, Ren SY (2018) Passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks with state coupling and spatial diffusion coupling. Neurocomputing 275:1208–1218

    Article  Google Scholar 

  52. Li CJ, Yu WW, Huang TW (2014) Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach. Neural Netw 54:85–94

    Article  MATH  Google Scholar 

  53. Xu BB, Huang YL, Wang JL, Wei PC, Ren SY (2016) Passivity of linearly coupled reaction–diffusion neural networks with switching topology and time-varying delay. Neurocomputing 182:274–283

    Article  Google Scholar 

  54. Xu BB, Huang YL, Wang JL, Wei PC, Ren SY (2016) Passivity of linearly coupled neural networks with reaction–diffusion terms and switching topology. J Franklin Inst 353(8):1882–1898

    Article  MathSciNet  MATH  Google Scholar 

  55. Wang JL, Wu HN, Guo L (2011) Passivity and stability analysis of reaction–diffusion neural networks with Dirichlet boundary conditions. IEEE Trans Neural Netw 22(12):2105–2116

    Article  Google Scholar 

  56. Lu JG (2008) Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitions Fractals 35(1):116–125

    Article  MathSciNet  MATH  Google Scholar 

  57. Wang JL, Wu HN (2012) Local and global exponential output synchronization of complex delayed dynamical detworks. Nonlinear Dyn 67(1):497–504

    Article  MATH  Google Scholar 

  58. Liang K, Dai MC, Shao H, Wang J, Wang Z, Chen B (2018) \({\cal{L}}_2 - {\cal{L}}_\infty \) synchronization for singularly perturbed complex networks with semi-Markov jump topology. Appl Math Comput 321:450–462

    MathSciNet  Google Scholar 

  59. Shen H, Huang X, Zhou JP, Wang Z (2012) Global exponential estimates for uncertain Markovian jump neural networks with reaction–diffusion terms. Nonlinear Dyn 69(1–2):473–486

    Article  MathSciNet  MATH  Google Scholar 

  60. Shen H, Li F, Yan HC, Karimi HR, Lam HK (2018) Finite-time event-triggered \({\cal{H}}_\infty \) control for T-S fuzzy Markov jump systems. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2788891

    Article  Google Scholar 

  61. Shen H, Li F, Xu SY, Sreeram V (2017) Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Trans Autom Control. https://doi.org/10.1109/TAC.2017.2774006

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. They also wish to express their sincere appreciation to Prof. Jinliang Wang for the fruitful discussions with him and good suggestions which helped to improve this paper. This work was supported in part by the National Natural Science Foundation of China under Grants 11501411, 61503010 and 61773285, in part by the open fund of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis (No. HCIC201704), and in part by the Fundamental Research Funds for the Central Universities (No.YWF-18-BJ-Y-108).

Author information

Authors and Affiliations

  1. School of Computer Science and Software Engineering, Tianjin Key Laboratory of Optoelectronic Detection Technology and System, Tianjin Polytechnic University, Tianjin, 300387, China

    Yanli Huang

  2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China

    Yanli Huang

  3. School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Weizhong Chen

  4. School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin, 300387, China

    Shunyan Ren

  5. School of of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, China

    Zewei Zheng

Authors
  1. Yanli Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weizhong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shunyan Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zewei Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zewei Zheng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Y., Chen, W., Ren, S. et al. Passivity and Synchronization of Coupled Reaction–Diffusion Cohen–Grossberg Neural Networks with Fixed and Switching Topologies. Neural Process Lett 49, 1433–1457 (2019). https://doi.org/10.1007/s11063-018-9879-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9879-4

Keywords

Search

Navigation