Bifurcation analysis and sliding mode control of fractional-order BAM neural network with multiple delays
Source abstract
Abstract
This paper investigates the bifurcation dynamics behavior of a fractional-order five-dimensional bidirectional associative memory neural network model incorporating multiple delays. Selecting the delay as the bifurcation parameter, the critical delay thresholds for the onset of Hopf bifurcation are derived through characteristic equation analysis. Furthermore, the interplay between independent and coupled delay effects is systematically explored, and bifurcation mechanisms under various delay interaction modes are discussed. To address oscillatory behavior typically observed after the bifurcation, a sliding mode control scheme is designed to ensure the asymptotic stability of the system. Finally, simulation results demonstrate the validity of the theoretical results and confirm the effectiveness of the control scheme in suppressing oscillatory divergence.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Neural Networks Stability and Synchronization · Neural Networks and Applications · stochastic dynamics and bifurcation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Physics and Electronic Information, Guangxi Minzu University , Nanning 530006,
Funding
National Natural Science Foundation of China
References (36)
Show source-provided references
1. H. Ramsauer , B.Schäfl, J.Lehner, P.Seidl, M.Widrich, T.Adler, L.Gruber, M.Holzleitner, M.Pavlović, G. K.Sandve, , “Hopfield networks is all you need,” arXiv:2008.02217 (2020).
2. Assessment of stacked unidirectional and bidirectional long short-term memory networks for electricity load forecasting10.1016/j.epsr.2020.106489 ↗
3. Bidirectional associative memories10.1109/21.87054 ↗
4. Image recognition using bidirectional associative memory and fuzzy image enhancement10.20428/jst.v19i1.763 ↗
5. Memristor-based BAM circuit implementation for image associative memory and filling-in10.1007/s00521-020-05538-7 ↗
6. A study on associative neural memories10.14569/ijacsa.2010.010619 ↗
7. Fractional differentiation by neocortical pyramidal neurons10.1038/nn.2212 ↗
8. A fractional-order visual neural network for collision sensing in noisy and dynamic scenes10.1016/j.asoc.2023.110897 ↗
9. New predefined-time stability theorem and synchronization of fractional-order memristive delayed BAM neural networks10.1016/j.cnsns.2025.108850 ↗
10. 2004
11. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays10.1103/physreve.80.026206 ↗
12. 2010
13. Exploration of bifurcation for a fractional-order BAM neural network with n + 2 neurons and mixed time delays10.1016/j.chaos.2022.112117 ↗
14. Complex spiking neural networks with synaptic time-delay based on anti-interference function10.1007/s11571-022-09803-4 ↗
15. A novel fractional-order neutral-type two-delayed neural network: Stability, bifurcation, and numerical solution10.1016/j.matcom.2025.01.001 ↗
16. Bifurcation study for fractional-order three-layer neural networks involving four time delays10.1007/s12559-021-09939-1 ↗
17. Bifurcations in a fractional-order BAM neural network with four different delays10.1016/j.neunet.2021.04.005 ↗
18. Bifurcation mechanism for fractional-order three-triangle multi-delayed neural networks10.1007/s11063-022-11130-y ↗
19. Bifurcation properties for fractional order delayed BAM neural networks10.1007/s12559-020-09782-w ↗
20. Robust state estimation for fractional-order delayed BAM neural networks via LMI approach10.1016/j.jfranklin.2020.01.028 ↗
21. Introduction to bifurcation theory10.1103/revmodphys.63.991 ↗
22. Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation10.1016/j.matcom.2020.11.023 ↗
23. Further investigation on bifurcation and their control of fractional-order bidirectional associative memory neural networks involving four neurons and multiple delays10.1002/mma.7581 ↗
24. Effects of multiple delays on dynamics of a five-neuron network model10.1007/s11071-018-4346-3 ↗
25. Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion10.1016/j.amc.2015.06.009 ↗
26. Fractional-order echo state network backstepping control of fractional-order nonlinear systems10.1109/tetci.2023.3309739 ↗
27. 2006
28. Remarks on fractional derivatives10.1016/j.amc.2006.08.163 ↗
29. Mittag–Leffler stability of fractional order nonlinear dynamic systems10.1016/j.automatica.2009.04.003 ↗
30. Stability analysis of linear fractional differential system with multiple time delays10.1007/s11071-006-9094-0 ↗
31. Synchronization and synchronized periodic solution in a simplified five-neuron BAM neural network with delays10.1016/j.neucom.2010.11.017 ↗
32. Probing into bifurcation for fractional-order BAM neural networks concerning multiple time delays10.1016/j.jocs.2022.101701 ↗
33. A further study on bifurcation for fractional order BAM neural networks with multiple delays10.1016/j.neucom.2020.08.047 ↗
34. Abzweigung einer periodischen lösung von einer
35. Bifurcation control of a fractional-order Van Der Pol oscillator based on the state feedback10.1002/asjc.995 ↗
36. Hybrid control on bifurcation for a delayed fractional gene regulatory network10.1016/j.chaos.2016.02.036 ↗