Novel fixed-time synchronization results of fractional-order fuzzy cellular neural networks with delays and interactions

Jun Liu; Wenjing Deng; Shuqin Sun; Kaibo Shi; Jun Liu; Wenjing Deng; Shuqin Sun; Kaibo Shi

doi:10.3934/math.2024646

AIMS Mathematics

2024, Volume 9, Issue 5: 13245-13264. doi: 10.3934/math.2024646

Previous Article Next Article

Research article Special Issues

Novel fixed-time synchronization results of fractional-order fuzzy cellular neural networks with delays and interactions

1.
School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China
2.
Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, Sichuan 610068, China
3.
School of Mathematics Education, China West Normal University, Nanchong Sichuan 637002, China
4.
School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, Sichuan 610106, China

Received: 18 February 2024 Revised: 26 March 2024 Accepted: 07 April 2024 Published: 10 April 2024
MSC : 37N35, 93D15, 93D21, 93D40

This research investigated the fixed-time (FXT) synchronization of fractional-order fuzzy cellular neural networks (FCNNs) with delays and interactions based on an enhanced FXT stability theorem. By conceiving proper Lyapunov functions and applying inequality techniques, several sufficient conditions were obtained to vouch for the fixed-time synchronization (FXTS) of the discussed systems through two categories of control schemes. Moreover, in terms of another FXT stability theorem, different upper-bounding estimating formulas for settling time (ST) were given, and the distinctions between them were pointed out. Two examples were delivered at length to demonstrate the conclusions.
- synchronization,
- adaptive control,
- fractional-order,
- neural networks,
- interactions
Citation: Jun Liu, Wenjing Deng, Shuqin Sun, Kaibo Shi. Novel fixed-time synchronization results of fractional-order fuzzy cellular neural networks with delays and interactions[J]. AIMS Mathematics, 2024, 9(5): 13245-13264. doi: 10.3934/math.2024646

Related Papers:

Abstract

This research investigated the fixed-time (FXT) synchronization of fractional-order fuzzy cellular neural networks (FCNNs) with delays and interactions based on an enhanced FXT stability theorem. By conceiving proper Lyapunov functions and applying inequality techniques, several sufficient conditions were obtained to vouch for the fixed-time synchronization (FXTS) of the discussed systems through two categories of control schemes. Moreover, in terms of another FXT stability theorem, different upper-bounding estimating formulas for settling time (ST) were given, and the distinctions between them were pointed out. Two examples were delivered at length to demonstrate the conclusions.

References

[1]	L. O. Chua, L. Yang, Cellular neural networks: theory, IEEE Trans. Circuits Syst., 35 (1988), 1257–1272. http://dx.doi.org/10.1109/31.7600 doi: 10.1109/31.7600
[2]	T. Yang, L. B. Yang, C. W. Wu, L. O. Chua, Fuzzy cellular neural networks: theory, In: 1996 Fourth IEEE International workshop on cellular neural networks and their applications proceedings (CNNA-96), Spain: IEEE, 1996,181–186. http://dx.doi.org/10.1109/CNNA.1996.566545
[3]	T. Yang, L. B. Yang, C. W. Wu, L. O. Chua, Fuzzy cellular neural networks: applications, In: 1996 Fourth IEEE International workshop on cellular neural networks and their applications proceedings (CNNA-96), Spain: IEEE, 1996,225–230. http://dx.doi.org/10.1109/CNNA.1996.566560
[4]	C. Lin, C. Yeh, S. Liang, J. Chung, N. Kumar, Support-vector-based fuzzy neural network for pattern classification, IEEE Trans. Fuzzy Syst., 14 (2006), 31–41. http://dx.doi.org/10.1109/TFUZZ.2005.861604 doi: 10.1109/TFUZZ.2005.861604
[5]	K. Ratnavelu, M. Kalpana, P. Balasubramaniam, K. Wong, P. Raveendran, Image encryption method based on chaotic fuzzy cellular neural networks, Signal Process., 140 (2017), 87–96. https://doi.org/10.1016/j.sigpro.2017.05.002 doi: 10.1016/j.sigpro.2017.05.002
[6]	J. Liu, L. Shu, Q. Chen, S. Zhong, Fixed-time synchronization criteria of fuzzy inertial neural networks via Lyapunov functions with indefinite derivatives and its application to image encryption, Fuzzy Sets Syst., 459 (2023), 22–42. https://doi.org/10.1016/j.fss.2022.08.002 doi: 10.1016/j.fss.2022.08.002
[7]	J. Liu, Q. Chen, D. Zhang, L. Shu, K. S. Shi, Novel finite-time synchronization results of fuzzy inertial neural networks via event-triggered control and its application to image encryption, Int. J. Fuzzy Syst., 25 (2023), 2779–2795. https://doi.org/10.1007/s40815-023-01530-0 doi: 10.1007/s40815-023-01530-0
[8]	P. Arena, R. Caponetto, L. Fortuna, D. Porto, Bifurcation and chaos in noninteger order cellular neural networks, Internat. J. Bifur. Chaos, 8 (1998), 1527–1539. https://doi.org/10.1142/S0218127498001170 doi: 10.1142/S0218127498001170
[9]	X. Yao, X. Liu, S. Zhong, Exponential stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks with multiple delays, Neurocomputing, 419 (2021), 239–250. https://doi.org/10.1016/j.neucom.2020.08.057 doi: 10.1016/j.neucom.2020.08.057
[10]	C. Jiyang, C. Li, X. Yang, Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects, J. Franklin Inst., 355 (2018), 7595–7608. https://doi.org/10.1016/j.jfranklin.2018.07.039 doi: 10.1016/j.jfranklin.2018.07.039
[11]	S. Tyagi, S. C. Martha, Finite-time stability for a class of fractional-order fuzzy neural networks with proportional delay, Fuzzy Sets Syst., 381 (2019), 68–77. https://doi.org/10.1016/j.fss.2019.04.010 doi: 10.1016/j.fss.2019.04.010
[12]	C. Aouiti, T. Farid, Global dissipativity of quaternion-valued fuzzy cellular fractional-order neural networks with time delays, Neural Process. Lett., 55 (2023), 481–503. https://doi.org/10.1007/s11063-022-10893-8 doi: 10.1007/s11063-022-10893-8
[13]	M. S. Ali, G. Narayanan, S. Saroha, B. Priya, G. K. Thakur, Finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks with time delay and leakage term, Math. Comput. Simul., 185 (2021), 468–485. https://doi.org/10.1016/j.matcom.2020.12.035 doi: 10.1016/j.matcom.2020.12.035
[14]	M. Zheng, L. Li, H. Peng, J. Xiao, Y. Yang, Y. Zhang, et al., Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks, Commun. Nonlinear Sci. Numer. Simul., 59 (2018), 272–291. https://doi.org/10.1016/j.cnsns.2017.11.025 doi: 10.1016/j.cnsns.2017.11.025
[15]	Y. Sun, Y. Liu, Fixed-time synchronization of delayed fractional-order memristor-based fuzzy cellular neural networks, IEEE Access, 8 (2020), 165951–165962. https://doi.org/10.1109/ACCESS.2020.3022928 doi: 10.1109/ACCESS.2020.3022928
[16]	M. S. Asl, M. Javidi, B. Ahmad, New predictor-corrector approach for nonlinear fractional differential equations: Error analysis and stability, J. Appl. Anal. Comput., 9 (2019), 1527–1557. https://doi.org/10.11948/2156-907X.20180309 doi: 10.11948/2156-907X.20180309
[17]	A. A. Alikhanov, M. S. Asl, C. Huang, A. Khibiev, A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay, J. Comput. Appl. Math., 438 (2024), 115515. https://doi.org/10.1016/j.cam.2023.115515 doi: 10.1016/j.cam.2023.115515
[18]	K. Liang, L. Wang, Exponential synchronization in inertial Cohen-Grossberg neural networks with time delays, J. Franklin Inst., 356 (2019), 11285–11304. https://doi.org/10.1016/j.jfranklin.2019.07.027 doi: 10.1016/j.jfranklin.2019.07.027
[19]	S. Yang, C. Hu, Y. Yu, H. Jiang, Exponential stability of fractional-order impulsive control systems with applications in synchronization, IEEE Trans. Cybernet., 50 (2020), 3157–3168. https://doi.org/10.1109/TCYB.2019.2906497 doi: 10.1109/TCYB.2019.2906497
[20]	W. Ma, C. Li, Y. Wu, Y. Wu, Synchronization of fractional fuzzy cellular neural networks with interactions, Chaos, 27 (2017), 103106. https://doi.org/10.1063/1.5006194 doi: 10.1063/1.5006194
[21]	T. Hu, X. Zhang, S. Zhong, Global asymptotic synchronization of nonidentical fractional-order neural networks, Neurocomputing, 313 (2018), 39–46. https://doi.org/10.1016/j.neucom.2018.05.098 doi: 10.1016/j.neucom.2018.05.098
[22]	P. Mani, R. Rajan, L. Shanmugam, Y. H. Joo, Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption, Inform. Sci., 491 (2019), 74–89. https://doi.org/10.1016/j.ins.2019.04.007 doi: 10.1016/j.ins.2019.04.007
[23]	J. Wang, X. Wang, X. Zhang, S. Zhu, Global h-synchronization for high-order delayed inertial neural networks via direct SORS strategy, IEEE Trans. Syst. Man Cybernet. Syst., 53 (2023), 6693–6704. https://doi.org/10.1109/TSMC.2023.3286095 doi: 10.1109/TSMC.2023.3286095
[24]	Z. Dong, X. Wang, X. Zhang, M. Hu, T. N. Dinh, Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption, Nonlinear Anal. Hybrid Syst., 47 (2023), 101291. https://doi.org/10.1016/j.nahs.2022.101291 doi: 10.1016/j.nahs.2022.101291
[25]	Z. Yang, J. Zhang, J. Hu, J. Mei, New results on finite-time stability for fractional-order neural networks with proportional delay, Neurocomputing, 442 (2021), 327–336. https://doi.org/10.1016/j.neucom.2021.02.082 doi: 10.1016/j.neucom.2021.02.082
[26]	Y. W. Wang, Y. Zhang, X. K. Liu, X. Chen, Distributed predefined-time optimization and control for multi-bus DC microgrid, IEEE Trans. Power Syst., 2023, 1–11. https://doi.org/10.1109/TPWRS.2023.3349165 doi: 10.1109/TPWRS.2023.3349165
[27]	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
[28]	C. Chen, L. Li, H. Peng, Y. Yang, L. Mi, H. Zhao, A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks, Neural Netw., 123 (2020), 412–419. https://doi.org/10.1016/j.neunet.2019.12.028 doi: 10.1016/j.neunet.2019.12.028
[29]	A. Abdurahman, H. Jiang, C. Hu, Improved fixed-time stability results and application to synchronization of discontinuous neural networks with state-dependent switching, Internat. J. Robust Nonlinear Control, 31 (2021), 5725–5744. https://doi.org/10.1002/rnc.5566 doi: 10.1002/rnc.5566
[30]	C. Hu, J. Yu, Z. Chen, H. Jiang, T. Huang, Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks, Neural Netw., 89 (2017), 74–83. https://doi.org/10.1016/j.neunet.2017.02.001 doi: 10.1016/j.neunet.2017.02.001
[31]	T. Jia, X. Chen, L. He, F. Zhao, J. Qiu, Finite-time synchronization of uncertain fractional-order delayed memristive neural networks via adaptive sliding mode control and its application, Fractal Fract., 6 (2022), 502. https://doi.org/10.3390/fractalfract6090502 doi: 10.3390/fractalfract6090502
[32]	X. Chen, T. Jia, Z. Wang, X. Xie, J. Qiu, Practical fixed-time bipartite synchronization of uncertain coupled neural networks subject to deception attacks via dual-channel event-triggered control, IEEE Trans. Cybernet., 2023, 1–11. https://doi.org/10.1109/TCYB.2023.3338165 doi: 10.1109/TCYB.2023.3338165
[33]	C. Chen, L. Li, H. Peng, Y. Yang, L. Mi, L. Wang, A new fixed-time stability theorem and its application to the synchronization control of memristive neural networks, Neurocomputing, 349 (2019), 290–300. https://doi.org/10.1016/j.neucom.2019.03.040 doi: 10.1016/j.neucom.2019.03.040
[34]	Y. Lei, Y. Wang, I. Morărescu, R. Postoyan, Event-triggered fixed-time stabilization of two time scales linear systems, IEEE Trans. Automat. Control, 68 (2023), 1722–1729. https://doi.org/10.1109/TAC.2022.3151818 doi: 10.1109/TAC.2022.3151818
[35]	M. Zheng, L. Li, H. Peng, J. Xiao, Y. Yang, Y. Zhang, et al., Fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay, J. Franklin Inst., 355 (2018), 6780–6809. https://doi.org/10.1016/j.jfranklin.2018.06.041 doi: 10.1016/j.jfranklin.2018.06.041
[36]	F. Kong, Q. Zhu, R. Sakthivel, A. Mohammadzadeh, Fixed-time synchronization analysis for discontinuous fuzzy inertial neural networks with parameter uncertainties, Neurocomputing, 422 (2021), 295–313. https://doi.org/10.1016/j.neucom.2020.09.014 doi: 10.1016/j.neucom.2020.09.014
[37]	Y. Liu, G. Zhang, J. Hu, Fixed-time stabilization and synchronization for fuzzy inertial neural networks with bounded distributed delays and discontinuous activation functions, Neurocomputing, 495 (2022), 86–96. https://doi.org/10.1016/j.neucom.2022.04.101 doi: 10.1016/j.neucom.2022.04.101
[38]	W. Wang, X. Jia, Z. Wang, X. Luo, L. Li, J. Kurths, et al., Fixed-time synchronization of fractional order memristive MAM neural networks by sliding mode control, Neurocomputing, 401 (2020), 364–376. https://doi.org/10.1016/j.neucom.2020.03.043 doi: 10.1016/j.neucom.2020.03.043
[39]	E. Arslan, G. Narayanan, M. S. Ali, S. Arik, S. Saroha, Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks with uncertain parameters and time-varying delays, Neural Netw., 130 (2020), 60–74. https://doi.org/10.1016/j.neunet.2020.06.021 doi: 10.1016/j.neunet.2020.06.021
[40]	Q. Gan, R. Xu, P. Yang, Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 433–443. https://doi.org/10.1016/j.cnsns.2011.05.014 doi: 10.1016/j.cnsns.2011.05.014
[41]	M. Roohi, C. Zhang, Y. Chen, Adaptive model-free synchronization of different fractional-order neural networks with an application in cryptography, Nonlinear Dyn., 100 (2020), 3979–4001. https://doi.org/10.1007/s11071-020-05719-y doi: 10.1007/s11071-020-05719-y
[42]	M. Roohi, C. Zhang, M. Taheri, A. Basse-O'Connor, Synchronization of fractional-order delayed neural networks using dynamic-free adaptive sliding mode control, Fractal Fract., 7 (2023), 682. https://doi.org/10.3390/fractalfract7090682 doi: 10.3390/fractalfract7090682
[43]	K. Mathiyalagan, J. H. Park, R. Sakthivel, Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities, Appl. Math. Comput., 259 (2015), 967–979. https://doi.org/10.1016/j.amc.2015.03.022 doi: 10.1016/j.amc.2015.03.022
[44]	Y. Liu, M. Liu, X. Xu, Adaptive control design for fixed-time synchronization of fuzzy stochastic cellular neural networks with discrete and distributed delay, Iran. J. Fuzzy Syst., 18 (2021), 13–28. https://doi.org/10.22111/ijfs.2021.6330 doi: 10.22111/ijfs.2021.6330
[45]	H. Ren, Z. Peng, Y. Gu, Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control, Neural Netw., 130 (2020), 165–175. https://doi.org/10.1016/j.neunet.2020.07.002 doi: 10.1016/j.neunet.2020.07.002
[46]	W. Sun, Y. Wu, J. Zhang, S. Qin, Inner and outer synchronization between two coupled networks with interactions, J. Franklin Inst., 352 (2014), 3166–3177. https://doi.org/10.1016/j.jfranklin.2014.08.004 doi: 10.1016/j.jfranklin.2014.08.004
[47]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, 204 (2006), 1–523.
[48]	B. Chen, J. Chen, Global asymptotical $\omega$-periodicity of a fractional-order non-autonomous neural networks, Neural Netw., 68 (2015), 78–88. https://doi.org/10.1016/j.neunet.2015.04.006 doi: 10.1016/j.neunet.2015.04.006
[49]	G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, 2 Eds., Cambridge: Cambridge University Press, 1952.

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)