Prespecified-time bipartite synchronization of coupled reaction-diffusion memristive neural networks with competitive interactions

Ruoyu Wei; Jinde Cao; Ruoyu Wei; Jinde Cao

doi:10.3934/mbe.2022598

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12814-12832. doi: 10.3934/mbe.2022598

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Prespecified-time bipartite synchronization of coupled reaction-diffusion memristive neural networks with competitive interactions

Ruoyu Wei ^{1
,
,},
Jinde Cao ^2,3

1.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Mathematics, Southeast University, Nanjing 210096, China
3.
Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea

Academic Editor: Xiaodi Li

Received: 01 June 2022 Revised: 25 July 2022 Accepted: 27 July 2022 Published: 01 September 2022

In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.
- memristor,
- reaction-diffusion term,
- neural networks,
- competitive interactions,
- bipartite synchronization,
- prespecified-time synchronization
Citation: Ruoyu Wei, Jinde Cao. Prespecified-time bipartite synchronization of coupled reaction-diffusion memristive neural networks with competitive interactions[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12814-12832. doi: 10.3934/mbe.2022598

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Abstract

In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.

References

[1]	L. O. Chua, Memristor-the missing circuit element, IEEE Trans. Circuit Theory., 18 (1971), 507–519. https://doi.org/10.1109/TCT.1971.1083337 doi: 10.1109/TCT.1971.1083337
[2]	D. Strukov, G. Snider, D. Stewart, R. S. Williams, The missing memristor found, Nature, 453 (2008), 80–83. https://doi.org/10.1038/nature06932 doi: 10.1038/nature06932
[3]	K. Miller, K. S. Nalwa, A. Bergerud, N. M. Neihart, S. Chaudhary, Memristive behavior in thin anodic titania, IEEE Electron Device Lett., 37 (2010), 737–739. https://doi.org/10.1109/LED.2010.2049092 doi: 10.1109/LED.2010.2049092
[4]	J. Sun, Y. Shen, Q. Yin, C. Xu, Compound synchronization of four memristor chaotic oscillator systems and secure communication, Chaos, 23 (2012), 1–10. https://doi.org/10.1063/1.4794794 doi: 10.1063/1.4794794
[5]	F. Corinto, A. Ascoli, M. Gilli, Nonlinear dynamics of memristor oscillators, IEEE Trans. Circuits Syst. I, 58 (2011), 1323–1336. https://doi.org/10.1109/TCSI.2010.2097731 doi: 10.1109/TCSI.2010.2097731
[6]	Y. V. Pershin, M. Di Ventra, Experimental demonstration of associative memory with memristive neural networks, Neural Netw., 23 (2010), 881–886. https://doi.org/10.1016/j.neunet.2010.05.001 doi: 10.1016/j.neunet.2010.05.001
[7]	L. Wang, H. He, Z. Zeng, Global synchronization of fuzzy memristive neural networks with discrete and distributed delays, IEEE Trans. Fuzz. Syst., 28 (2020), 2022–2034. https://doi.org/10.1109/TFUZZ.2019.2930032 doi: 10.1109/TFUZZ.2019.2930032
[8]	R. Wei, J. Cao, W. Qian, C. Xue, X. Ding, Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method, AIMS Math., 6 (2021), 6915–6932. https://doi.org/10.3934/math.2021405 doi: 10.3934/math.2021405
[9]	L. Wang, Z. Zeng, M. Ge, A disturbance rejection framework for finite-time and fixed-time stabilization of delayed memristive neural networks, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 905–915. https://doi.org/10.1109/TSMC.2018.2888867 doi: 10.1109/TSMC.2018.2888867
[10]	Y. Sheng, H. Zhang, Z. Zeng, Stability and robust stability of stochastic reaction-diffusion neural networks with infinite discrete and distributed delays, IEEE Trans. Syst. Man. Cybern. Syst., 50 (2020), 1721–1732. https://doi.org/10.1109/TSMC.2017.2783905 doi: 10.1109/TSMC.2017.2783905
[11]	Y. Sheng, Z. Zeng, Passivity and robust passivity of stochastic reaction-diffusion neural networks with time-varying delays, J. Franklin Inst., 354 (2017), 3995–4012. https://doi.org/10.1016/j.jfranklin.2017.03.014 doi: 10.1016/j.jfranklin.2017.03.014
[12]	Z. Wang, J. Cao, G. Lu, M. Abdel-Aty, Fixed-time passification analysis of interconnected memristive reaction-diffusion neural networks, IEEE Trans. Netwowk Sci. Eng., 7 (2020), 1814–1824. https://doi.org/10.1109/TNSE.2019.2954463 doi: 10.1109/TNSE.2019.2954463
[13]	Z. Guo, S. Wang, J. Wang, Global exponential synchronization of coupled delayed memristive neural networks with reaction-diffusion terms via distributed pinning controls, IEEE Trans. Neural Networks Learn. Syst., 32 (2021), 105–116. https://doi.org/10.1109/TNNLS.2020.2977099 doi: 10.1109/TNNLS.2020.2977099
[14]	X. Yang, J. Cao, Z. Yang, Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pining-impulsive controller, Siam J. Control Optim., 51 (2013), 3486–3510. https://doi.org/10.1137/120897341 doi: 10.1137/120897341
[15]	C. Altafini, Consensus problems on networks with antagonistic interactions, IEEE Trans. Autom. Control, 58 (2013), 935–946. https://doi.org/10.1109/TAC.2012.2224251 doi: 10.1109/TAC.2012.2224251
[16]	J. Hu, Y. Wu, T. Li, B. K. Ghosh, Consensus control of general linear multiagent systems with antagonistic interactions and communication noises, IEEE Trans. Autom. Control, 64 (2019), 2122–2127. https://doi.org/10.1109/TAC.2018.2872197 doi: 10.1109/TAC.2018.2872197
[17]	Y. Wu, L. Liu, J. Hu, G. Feng, Adaptive antisynchronization of multilayer reaction-diffusion neural networks, IEEE Trans. Neural Netw. Learn. Syst., 29 (2018), 807–818. https://doi.org/10.1109/TNNLS.2017.2647811 doi: 10.1109/TNNLS.2017.2647811
[18]	F. Liu, Q. Song, G. Wen, J. Cao, X. Yang, Bipartite synchronization in coupled delayed neural networks under pinning control, Neural Networks, 108 (2018), 146–154. https://doi.org/10.1016/j.neunet.2018.08.009 doi: 10.1016/j.neunet.2018.08.009
[19]	N. Li, W. Zheng, Bipartite synchronization of multiple memristor-based neural networks with antagonistic interactions, IEEE Trans. Neural Networks Learn. Syst., 32 (2021), 1642–1653. https://doi.org/10.1109/TNNLS.2020.2985860 doi: 10.1109/TNNLS.2020.2985860
[20]	N. Li, W. Zheng, Bipartite synchronization for inertia memristor-based neural networks on coopetition networks, Neural Networks, 124 (2020), 39–49. https://doi.org/10.1016/j.neunet.2019.11.010 doi: 10.1016/j.neunet.2019.11.010
[21]	K. Mao, X. Liu, J. Cao, Y. Hu, Finite-time bipartite synchronization of coupled neural networks with uncertain parameters, Phys. A, 585 (2022), 126431. https://doi.org/10.1016/j.physa.2021.126431 doi: 10.1016/j.physa.2021.126431
[22]	X. Li, D. Peng, J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Autom. Control, 65 (2020), 4908–4913. https://doi.org/10.1109/TAC.2020.2964558 doi: 10.1109/TAC.2020.2964558
[23]	X. Li, X. Yang, J. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 117 (2020), 108981. https://doi.org/10.1016/j.automatica.2020.108981 doi: 10.1016/j.automatica.2020.108981
[24]	S. P. Bhat, D. S. Bernstein, Finite-time stability of continuous autonomous systems, Siam J. Control Optim., 38 (2000), 751–766. https://doi.org/10.1137/S0363012997321358 doi: 10.1137/S0363012997321358
[25]	X. Li, D. W. C. Ho, J. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368. https://doi.org/10.1016/j.automatica.2018.10.024 doi: 10.1016/j.automatica.2018.10.024
[26]	Z. Zhang, X. Liu, D. Zhou, C. Lin, J. Chen, H. Wang, Finite-time stabilizability and instabilizability for complex-valued memristive neural networks with time delays, IEEE Trans. Syst. Man Cybern. Syst., 48 (2018), 2371–2382. https://doi.org/10.1109/TSMC.2017.2754508 doi: 10.1109/TSMC.2017.2754508
[27]	L. Feng, J. Yu, C. Hu, C. Yang, H. Jiang, Nonseparation method-based finite/fixed-time synchronization of fully complex-valued discontinuous neural networks, IEEE Trans. Cybern., 51 (2021), 3212–3223. https://doi.org/10.1109/TCYB.2020.2980684 doi: 10.1109/TCYB.2020.2980684
[28]	A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Trans. Automat. Control, 57 (2012), 2106–2110. https://doi.org/10.1109/TAC.2011.2179869 doi: 10.1109/TAC.2011.2179869
[29]	R. Wei, J. Cao, Fixed-time synchronization of second-order MNNs in quaternion field, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 3587–3598. https://doi.org/10.1109/TSMC.2019.2931091 doi: 10.1109/TSMC.2019.2931091
[30]	C. Hu, H. Jiang, Special functions-based fixed-time estimation and stabilization for dynamic systems, IEEE Trans. Syst. Man Cybern. Syst., 52 (2022), 3251–3262. https://doi.org/10.1109/TSMC.2021.3062206 doi: 10.1109/TSMC.2021.3062206
[31]	X. Ding, J. Cao, A. Alsaedi, T. Hayat, Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions, Neural Networks, 90 (2017), 42–55. https://doi.org/10.1016/j.neunet.2017.03.006 doi: 10.1016/j.neunet.2017.03.006
[32]	C. Hu, H. He, H. Jiang, Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control, Neural Networks, 146 (2022), 341–349. https://doi.org/10.1016/j.neunet.2021.11.023 doi: 10.1016/j.neunet.2021.11.023
[33]	C. Hu, H. He, H. Jiang, Fixed/preassigned-time synchronization of complex networks via improving fixed-Time stability, IEEE Trans. Cybern., 51 (2021), 2882–2892. https://doi.org/10.1109/TCYB.2020.2977934 doi: 10.1109/TCYB.2020.2977934
[34]	S. Shao, X. Liu, J. Cao, Prespecified-time synchronization of switched coupled neural networks via smooth controllers, Neural Networks, 133 (2021), 32–39. https://doi.org/10.1016/j.neunet.2020.10.007 doi: 10.1016/j.neunet.2020.10.007
[35]	X. Liu, D. W. C. Ho, and C. Xie, Prespecified-time cluster synchronization of complex networks via a smooth control approach, IEEE Trans. Cybern., 50 (2020), 1771–1775. https://doi.org/10.1109/TCYB.2018.2882519 doi: 10.1109/TCYB.2018.2882519

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