Projective Synchronization of Quaternion-Valued Discontinuous Competitive Neural Networks with Multiple Time Scales

Yu Zheng; Ruoyu Wei; Zixuan Chen

doi:10.53941/ams.2025.100002

Abstract

In this study, we explore the projective synchronization of quaternion-valued competitive neural networks with multiple time scales (QVMTSCNNs), while analyzing the impacts of discontinuous activation functions and time delays. To achieve the control goal, two novel quaternion controllers are designed, which do not depend on the ratio of the fast and slow time scales. By applying the nonsmooth analysis and quaternion inequality techniques, two novel theorems for projective synchronization of QVMTSCNNs are derived by non-separating methods. The obtained results in this study are relatively simpler and straightforward, extending some previous findings. Lastly, numerical analyses are executed to substantiate the theoretical conclusions.

References

1.
Guo, R.; Lu, J.; Li, Y.; et al. Fixed-time synchronization of inertial complex-valued neural networks with time delays. Nonlinear Dyn. 2021, 105, 1643–1656.
2.
Chen, J.; Chen, B.; Zeng, Z. Global asymptotic stability and adaptive ultimate mittag–leffler synchronization for a fractional-order complex-valued memristive neural networks with delays. IEEE Trans. Syst. Man Cybern. Syst. 2018, 49, 2519–2535.
3.
Chen, D.; Zhang, W.; Cao, J.; et al. Fixed time synchronization of delayed quaternion-valued memristor-based neural networks. Adv. Differ. Equ. 2020, 2020, 1–16
4.
Feng, L.; Hu, C.; Yu, J.; et al. Fixed-time synchronization of coupled memristive complex-valued neural networks. Chaos Solitons Fractals 2021, 148, 110993.
5.
El Alami, A.; Berrahou, N.; Lakhili, Z.; et al. Efficient color face recognition based on quaternion discrete orthogonal moments neural networks. Multimed. Tools Appl. 2022, 81, 7685–7710.
6.
Cui, Y.; Takahashi, K.; Hashimoto, M. Design of control systems using quaternion neural network and its application to inverse kinematics of robot manipulator. In Proceedings of the 2013 IEEE/SICE International Symposium on System Integration, Kobe, Japan, 15–17 December 2013; pp. 527–532.
7.
Serrano, F.; Castillo, O.; Alassafi, M.; et al. Terminal sliding mode attitude-position quaternion based control of quadrotor unmanned aerial vehicle. Adv. Space Res. 2023, 71, 3855–3867.
8.
Wei, W.; Yu, J.; Wang, L.; et al. Fixed/preassigned-time synchronization of quaternion-valued neural networks via pure power-law control. Neural Netw. 2022, 146, 341–349.
9.
Zhang, J.; Ma, X.; Li, Y.; et al. Synchronization in fixed/preassigned-time of delayed fully quaternion-valued memristive neural networks via non-separation method. Commun. Nonlinear Sci. Numer. Simul. 2022, 113, 106581.
10.
Wei, R.; Cao, J. Fixed-time synchronization of quaternion-valued memristive neural networks with time delays. Neural Netw. 2019, 113, 1–10.
11.
Tu, Z.; Cao, J.; Hayat, T. Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks. Neural Netw. 2016, 75, 47–55.
12.
Cohen, M.A.; Grossberg, S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 1983, 13, 815–826.
13.
Zheng, C.; Hu, C.; Yu, J.; et al. Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays. Neural Netw. 2022, 153, 192–203.
14.
Lou, X.; Cui, B. Synchronization of competitive neural networks with different time scales. Phys. A Stat. Mech. Its Appl. 2007, 380, 563–576.
15.
Duan, L.; Fang, X.; Yi, X.; et al. Finite-time synchronization of delayed competitive neural networks with discontinuous neuron activations. Int. J. Mach. Learn. Cybern. 2018, 9, 1649–1661.
16.
Yang, X.; Li, C.; Song, Q.; et al. Global mittag-leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw. 2018, 105, 88–103.
17.
Pratap, A.; Raja, R.; Cao, J.; et al. Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of mittag leffler function. J. Frankl. Inst. 2019, 356, 2212–2239.
18.
Pecora, L.M.; Carroll, T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990, 64, 821.
19.
Wang, P.; Wen, G.; Yu, X.; et al. Synchronization of multi-layer networks: From node-to-node synchronization to complete synchronization. IEEE Trans. Circuits Syst. I Regul. Pap. 2018, 66, 1141–1152.
20.
Guo, R. Projective synchronization of a class of chaotic systems by dynamic feedback control method. Nonlinear Dyn. 2017, 90, 53–64.
21.
Zhang, G.; Hu, J.; Shen, Y. Exponential lag synchronization for delayed memristive recurrent neural networks. Neurocom-puting 2015, 154, 86–93.
22.
Petkovic, T.; Pribani ´ c, T.; Ðonli ´ c, M.; et al. Software synchronization of projector and camera for structured light 3d body scanning. In Proceedings of the 7th International Conference on 3D Body Scanning Technologies, Lugano, Switzerland, 30 November–1 December 2016.
23.
Gupta, H.; Jin, K.H.; Nguyen, H.Q.; et al. Cnn-based projected gradient descent for consistent ct image reconstruction. IEEE Trans. Med. Imaging 2018, 37, 1440–1453.
24.
Liu, Y.; Wang, Z.; Ma, Q.; et al. Multistability analysis of delayed recurrent neural networks with a class of piecewise nonlinear activation functions. Neural Netw. 2022, 152, 80–89.
25.
Ghosh, D. Time scale synchronization between two different time-delayed systems. Electron. J. Theor. Phys. 2009, 6, 125–138.
26.
Yang, W.; Wang, Y.W.; Morarescu, I.C.; et al. Fixed-time synchronization of competitive neural networks with multiple time scales. IEEE Trans. Neural Netw. Learn. Syst. 2021, 33, 4133–4138.
27.
Huang, Q.; Yu, Y.; Cao, J. Projective synchronization of inertial quaternion-valued neural networks via non-reduced order approach. Neural Process. Lett. 2024, 56, 21.
28.
Kumar, R.; Sarkar, S.; Das, S.; et al. Projective synchronization of delayed neural networks with mismatched parameters and impulsive effects. IEEE Trans. Neural Netw. Learn. Syst. 2019, 31, 1211–1221.
29.
Jiang, C.; Tang, Z.; Park, J.H.; et al. Matrix measure-based projective synchronization on coupled neural networks with clustering trees. IEEE Trans. Cybern. 2021, 53, 1222–1234.
30.
Cloud, M.J.; Drachman, B.C.; Lebedev, L. Inequalities; Springer: Berlin/Heidelberg, Germany, 1998.
31.
Peng, T.; Qiu, J.; Lu, J.; et al. Finite-time and fixed-time synchronization of quaternion-valued neural networks with/without mixed delays: An improved one-norm method. IEEE Trans. Neural Netw. Learn. Syst. 2021, 33, 7475–7487.
32.
Liu, X.; Chen, T. Finite-time and fixed-time cluster synchronization with or without pinning control. IEEE Trans. Cybern. 2016, 48, 240–252.
33.
Deng, H.; Bao, H. Fixed-time synchronization of quaternion-valued neural networks. Phys. A Stat. Mech. Its Appl. 2019,527, 121351.
34.
Aouiti, C.; Bessifi, M. Periodically intermittent control for finite-time synchronization of delayed quaternion-valued neuralnetworks. Neural Comput. Appl. 2021, 33, 6527–6547.
35.
Ansari, M.S.H.; Malik, M. Projective synchronization of fractional order quaternion valued uncertain competitive neuralnetworks. Chin. J. Phys. 2024, 88, 740–755.

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