Skip to main content
SpringerLink
Log in

Bipartite quasi-synchronization of multiple neural networks with generalized cooperative-competitive topology

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

This study examines the bipartite quasi-synchronization (B-Q synchronization) issue of coupled networks with general cooperative-competitive topology and the event-triggered communications between nodes to curb the communication cost. In the existing literature concerning bipartite synchronization, the network topology is required to be structurally balanced, which necessitates that competitive interactions exist only between two distinct subgroups. In this study, we aim to lengthen the network’s topology to a more general signed network in which antagonistic interactions can exist in the same or different subgroups. According to signed graph theory and the markovian stochastic event-triggering mechanism, the dynamical model of multiple neural networks (MNNs) with structurally unbalanced and markovian event-triggered communication is established. By utilizing the stochastic Lyapunov stability analysis, some adequate criteria for B-Q synchronization of MNNs with the structurally unbalanced graph are obtained; also, a bound for the B-Q synchronization error is provided. As a special case, the bipartite synchronization criteria for MNNs with the structurally balanced graph are also obtained. Finally, two simulations are performed to verify the theoretical result.

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.

Institutional subscriptions

References

  1. Cao J, Li L. Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Networks, 2009, 22: 335–342

    Article  MATH  Google Scholar 

  2. Yang X S, Liu Y, Cao J D, et al. Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching. IEEE Trans Neural Networks Learn Syst, 2020, 31: 5483–5496

    Article  MathSciNet  Google Scholar 

  3. Qi Q, Yang X, Xu Z, et al. Novel LKF method on H∞ synchronization of switched time-delay systems. IEEE Trans Cybern, 2022

  4. Wu W, Chen T P. Global synchronization criteria of linearly coupled neural network systems with time-varying coupling. IEEE Trans Neural Netw, 2008, 19: 319–332

    Article  Google Scholar 

  5. Yang X S, Cao J D, Lu J Q. Synchronization of randomly coupled neural networks with markovian jumping and time-delay. IEEE Trans Circuits Syst I Reg Papers, 2013, 60: 363–376

    Article  MathSciNet  MATH  Google Scholar 

  6. Lu J, Ho D W C, Cao J, et al. Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans Neural Netw, 2011, 22: 329–336

    Article  Google Scholar 

  7. Xu Y, Sun J, Wang, G, et al. Dynamic triggering mechanisms for distributed adaptive synchronization control and its application to circuit systems. IEEE Trans Circuits Syst I Reg Papers, 2021, 68: 2246–2256

    Article  MathSciNet  Google Scholar 

  8. Xu Y H, Wu X Q, Mao B, et al. Finite-time intra-layer and inter-layer quasi-synchronization of two-layer multi-weighted networks. IEEE Trans Circuits Syst I Reg Papers, 2021, 68: 1589–1598

    Article  MathSciNet  Google Scholar 

  9. Zhou S L, Wang S L, Liu W, et al. Cooperative attitude control in rigid body swarms based on group consensus. Sci Sin Tech, 2020, 50: 493–505

    Article  Google Scholar 

  10. Lee S H. Predator’s attack-induced phase-like transition in prey flock. Phys Lett A, 2006, 357: 270–274

    Article  Google Scholar 

  11. Grossberg S. Competition, decision, and consensus. J Math Anal Appl, 1978, 66: 470–493

    Article  MathSciNet  MATH  Google Scholar 

  12. Altafini C. Dynamics of opinion forming in structurally balanced social networks. PLoS ONE, 2012, 7: e38135

    Article  Google Scholar 

  13. Altafini C. Consensus problems on networks with antagonistic interactions. IEEE Trans Automat Contr, 2013, 58: 935–946

    Article  MathSciNet  MATH  Google Scholar 

  14. Valcher M E, Misra P. On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Syst Control Lett, 2014, 66: 94–103

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang H, Chen J. Bipartite consensus of linear multi-agent systems over signed digraphs: An output feedback control approach. IFAC Proc Volumes, 2014, 47: 4681–4686

    Article  Google Scholar 

  16. Hu J, Zheng W X. Emergent collective behaviors on coopetition networks. Phys Lett A, 2014, 378: 1787–1796

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang J, Hong Y, Wang J, et al. Cooperative and competitive multiagent systems: From optimization to games. IEEE CAA J Autom Sin, 2022, 9: 763–783

    Article  Google Scholar 

  18. Li N, Zheng W X. Bipartite synchronization for inertia memristor-based neural networks on coopetition networks. Neural Networks, 2020, 124: 39–49

    Article  MATH  Google Scholar 

  19. Zou Y, Su H, Tang R, et al. Finite-time bipartite synchronization of switched competitive neural networks with time delay via quantized control. ISA Trans, 2022, 125: 156–165

    Article  Google Scholar 

  20. Li N, Zheng W X. Bipartite synchronization of multiple memristor-based neural networks with antagonistic interactions. IEEE Trans Neural Networks Learn Syst, 2020, 32: 1642–1653

    Article  MathSciNet  Google Scholar 

  21. Wu Y Z, Liu L, Feng G. Adaptive antisynchronization of multilayer reaction—diffusion neural networks. IEEE Trans Neural Networks Learn Syst, 2017, 29: 807–818

    Article  MathSciNet  Google Scholar 

  22. Wu Y Z, Zhao Y Y, Hu J P. Bipartite consensus control of high-order multiagent systems with unknown disturbances. IEEE Trans Syst Man Cybern A, 2017, 49: 2189–2199

    Article  Google Scholar 

  23. Liu F, Song Q, Wen G, et al. Bipartite synchronization in coupled delayed neural networks under pinning control. Neural Networks, 2018, 108: 146–154

    Article  MATH  Google Scholar 

  24. Xu D, Pang J, Su H. Bipartite synchronization of signed networks via aperiodically intermittent control based on discrete-time state observations. Neural Networks, 2021, 144: 307–319

    Article  Google Scholar 

  25. Hu A H, Park J H, Cao J D, et al. Event-triggered bipartite consensus over cooperation-competition networks under DoS attacks. Sci China Tech Sci, 2021, 64: 157–168

    Article  Google Scholar 

  26. Miao B, Li X, Lou J, et al. Pinning bipartite synchronization for coupled reaction-diffusion neural networks with antagonistic interactions and switching topologies. Neural Networks, 2021, 141: 174–183

    Article  Google Scholar 

  27. Wang J, Xing M, Cao J, et al. H∞ bipartite synchronization of double-layer markov switched cooperation-competition neural networks: A distributed dynamic event-triggered mechanism. IEEE Trans Neural Netw Learn Syst, 2023, 34: 278–289

    Article  MathSciNet  Google Scholar 

  28. Li Q, Xia L, Song R, et al. Leader-follower bipartite output synchronization on signed digraphs under adversarial factors via data-based reinforcement learning. IEEE Trans Neural Networks Learn Syst, 2020, 31: 4185–4195

    Article  MathSciNet  Google Scholar 

  29. Sun W, Li B, Guo W, et al. Interval bipartite synchronization of multiple neural networks in signed graphs. IEEE Trans Neural Netw Learn Syst, 2022

  30. Zhai S D. Modulus synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies. Commun Nonlinear Sci Numer Simulat, 2016, 33: 184–193

    Article  MathSciNet  MATH  Google Scholar 

  31. Liang K, He W L, Xu J, et al. Impulsive effects on synchronization of singularly perturbed complex networks with semi-markov jump topologies. IEEE Trans Syst Man Cybern A, 2021, 52: 3163–3173

    Article  Google Scholar 

  32. Zhai S D, Li Q D. Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and switching topologies. Syst Control Lett, 2016, 94: 127–132

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhao G L, Wang Y F, Fu X W. Hybrid event-triggered consensus tracking of multi-agent systems with discrete control update. IEEE Trans Circuits Syst II, 2022, 69: 2206–2210

    Google Scholar 

  34. Lv S, He W, Qian F, et al. Leaderless synchronization of coupled neural networks with the event-triggered mechanism. Neural Networks, 2018, 105: 316–327

    Article  MATH  Google Scholar 

  35. Shi S, Wang Z, Song Q, et al. Leader-following quasi-bipartite synchronization of coupled heterogeneous harmonic oscillators via event-triggered control. Appl Math Computa, 2022, 427: 127172

    Article  MathSciNet  MATH  Google Scholar 

  36. Xing X, Liu J. Event-triggered neural network control for a class of uncertain nonlinear systems with input quantization. Neurocomputing, 2021, 440: 240–250

    Article  Google Scholar 

  37. Yao L, Huang X. Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks. Sci China Tech Sci, 2023, 66: 468–480

    Article  Google Scholar 

  38. Xu Z, Tang R, Sun Y, et al. Secure synchronization of coupled systems via double event-triggering mechanisms with actuator fault. IEEE Trans Netw Sci Eng, 2022, 9: 3580–3589

    Article  MathSciNet  Google Scholar 

  39. Mitrinovic D S, Pecaric J, Fink A M. Classical and New Inequalities in Analysis. London: Springer Science & Business Media, 1993

    Book  MATH  Google Scholar 

  40. Cai B, Weng R, Zhang R X, et al. Stabilization of a class of fuzzy stochastic jump systems with partial information on jump and sojourn parameters. Sci China Tech Sci, 2021, 64: 353–363

    Article  Google Scholar 

  41. Zhang L, Cai B, Tan T, et al. Stabilization of non-homogeneous hidden semi-Markov Jump systems with limited sojourn-time information. Automatica, 2020, 117: 108963

    Article  MathSciNet  MATH  Google Scholar 

  42. Shi Y, Li L, Yang J, et al. Center-based transfer feature learning with classifier adaptation for surface defect recognition. Mech Syst Signal Process, 2023, 188: 110001

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450046, China

    Ning Li

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    JinDe Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, Korea

    JinDe Cao

Authors
  1. Ning Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JinDe Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ning Li or JinDe Cao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62073122, 61833005 and 11872175), the Outstanding Youth Science Foundation Project of Henan Province (Grant No. 222300420022), and the Key Program of Higher Education of Henan Province (Grant No. 21A120001).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, N., Cao, J. Bipartite quasi-synchronization of multiple neural networks with generalized cooperative-competitive topology. Sci. China Technol. Sci. 66, 1855–1866 (2023). https://doi.org/10.1007/s11431-022-2392-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-022-2392-2

Search

Navigation