Exponential stability and synchronisation of fuzzy Mittag–Leffler discrete-time Cohen–Grossberg neural networks with time delays

References

• Abdelaziz, M., & Chérif, F. (2020). Piecewise asymptotic almost periodic solutions for impulsive fuzzy Cohen–Grossberg neural networks. Chaos, Solitons & Fractals, 132(1), Article number: 109575. https://doi.org/10.1016/j.chaos.2019.109575
   Web of Science ®Google Scholar
• Agarwal, R., Hristova, S., & O'Regan, D. (2019). Mittag–Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays. Mathematica Slovaca, 69(3), 583–598. https://doi.org/10.1515/ms-2017-0249
   Web of Science ®Google Scholar
• Ali, M. S., Narayanan, G., Shekher, V., Alsaedi, A., & Ahmad, B. (2020). Global Mittag–Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays. Communications In Nonlinear Science And Numerical Simulation, 83, Article number: 105088. https://doi.org/10.1016/j.cnsns.2019.105088
   Web of Science ®Google Scholar
• Aouiti, C., Assali, E. A., & El Foutayeni, Y. (2019). Finite-time and fixed-time synchronization of inertial Cohen–Grossberg-type neural networks with time varying delays. Neural Processing Letters, 50(3), 2407–2436. https://doi.org/10.1007/s11063-019-10018-8
   Web of Science ®Google Scholar
• Aouiti, C., Dridi, F., Hui, Q., & Moulay, E. (2021). (μ,ν)-pseudo almost automorphic solutions of neutral type Clifford-valued high-order hopfield neural networks with D-operator. Neural Processing Letters, 53(1), 799–828. https://doi.org/10.1007/s11063-020-10421-6
   Web of Science ®Google Scholar
• Butcher, J. C. (2016). Numerical methods for ordinary differential equations. Wiley.
   Google Scholar
• Calvo, M. P., & Palencia, C. (2006). A class of explicit multistep exponential integrators for semilinear problems. Numerische Mathematik, 102(3), 367–381. https://doi.org/10.1007/s00211-005-0627-0
   Web of Science ®Google Scholar
• Chen, L., Yin, H., Huang, T., Yuan, L., Zheng, S., & Yin, L. (2020). Chaos in fractional-order discrete neural networks with application to image encryption. Neural Networks, 125(3), 174–184. https://doi.org/10.1016/j.neunet.2020.02.008
   PubMed Web of Science ®Google Scholar
• Cheng, S., Ji, J. C., & Zhou, J. (2013). Fast synchronization of directionally coupled chaotic systems. Applied Mathematical Modelling, 37(1–2), 127–136. https://doi.org/10.1016/j.apm.2012.02.018
   Web of Science ®Google Scholar
• Cohen, M. A., & Grossberg, S. (1983). Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 13(5), 815–826. https://doi.org/10.1109/TSMC.1983.6313075
   Web of Science ®Google Scholar
• Dai, X. J., & Xiao, A. G. (2021). A note on Euler method for the overdamped generalized Langevin equation with fractional noise. Applied Mathematics Letters, 111, Article number: 106669. https://doi.org/10.1016/j.aml.2020.106669
   PubMed Web of Science ®Google Scholar
• El-Saka, H. A. A., Lee, S., & Jang, B. (2019). Dynamic analysis of fractional-order predator-prey biological economic system with Holling type II functional response. Nonlinear Dynamics, 96(1), 407–416. https://doi.org/10.1007/s11071-019-04796-y
   Web of Science ®Google Scholar
• Fěckan, M., & Wang, J. R. (2019). Periodic impulsive fractional differential equations. Advances in Nonlinear Analysis, 8(1), 482–496. https://doi.org/10.1515/anona-2017-0015
   Web of Science ®Google Scholar
• Garrappa, R., & Popolizio, M. (2011). Generalized exponential time differencing methods for fractional order problems. Computers and Mathematics with Applications, 62(3), 876–890. https://doi.org/10.1016/j.camwa.2011.04.054
   Web of Science ®Google Scholar
• Guo, B. L., Pu, X. K., & Huang, F. H. (2011). Fractional partial differential equations and their numerical solutions. Science Press.
   Google Scholar
• Hochbruck, M., Ostermann, A., & Schweitzer, J. (2009). Exponential Rosenbrock-type methods. SIAM Journal on Numerical Analysis, 47(1), 786–803. https://doi.org/10.1137/080717717
   Web of Science ®Google Scholar
• Hu, J., & Wang, J. (2015). Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays. Neural Networks, 66, 119–130. https://doi.org/10.1016/j.neunet.2015.03.001
   PubMed Web of Science ®Google Scholar
• Hu, L. Y., Ren, Y., & H. J. Yang (2019). Exponential synchronization of stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. Neurocomputing, 350, 13–19. https://doi.org/10.1016/j.neucom.2019.03.064
   Web of Science ®Google Scholar
• Hu, P., & Huang, C. M. (2021). Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method. Journal of Computational and Applied Mathematics, 382(2017), 113068. https://doi.org/10.1016/j.cam.2020.113068
   Web of Science ®Google Scholar
• Huang, Z. K., Mohamad, S., & Gao, F. (2014). Multi-almost periodicity in semi-discretizations of a general class of neural networks. Mathematics and Computers in Simulation, 101(7), 43–60. https://doi.org/10.1016/j.matcom.2013.05.017
   Web of Science ®Google Scholar
• Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Elsevier.
   Google Scholar
• Kong, F., & Rajan, R. (2021). Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen–Grossberg neural networks with uncertain external perturbations and mixed time delays. Fuzzy Sets and Systems, 411(4), 105–135. https://doi.org/10.1016/j.fss.2020.07.009
   Web of Science ®Google Scholar
• Kumar, D., Singh, J., Tanwar, K., & Baleanu, D. (2019). A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag–Leffler laws. International Journal of Heat and Mass Transfer, 138(8), 1222–1227. https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.094
   Web of Science ®Google Scholar
• Lakshmanan, S., Prakash, M., Lim, C. P., Rakkiyappan, R., Balasubramaniam, P., & Nahavandi, S. (2018). Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Transactions on Neural Networks and Learning Systems, 29(1), 195–207. https://doi.org/10.1109/TNNLS.2016.2619345
   PubMed Web of Science ®Google Scholar
• Li, R. X., Cao, J. D., Alsaedi, A., Ahmad, B., Alsaadi, F. E., & Hayat, T. (2016). Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen-Grossberg neural networks. Complexity, 21(S2), 459–469. https://doi.org/10.1002/cplx.v21.S2
   Web of Science ®Google Scholar
• Li, Y. K., & Zhang, T. W. (2015). Global exponential stability and existence of anti-periodic solutions to impulsive Cohen-Grossberg neural networks on time scales. Topological Methods In Nonlinear Analysis, 45(2), 363–384. https://doi.org/10.12775/TMNA.2015.018
   Web of Science ®Google Scholar
• Liu, P., Zeng, Z. G., & Wang, J. (2019). Global synchronization of coupled fractional-order recurrent neural networks. IEEE Transactions on Neural Networks and Learning Systems, 30(8), 2358–2368. https://doi.org/10.1109/TNNLS.5962385
   PubMed Web of Science ®Google Scholar
• Ostermann, A., Thalhammer, M., & Wright, W. M. (2006). A class of exponential general linear methods. BIT Numerical Mathematics, 46(2), 409–431. https://doi.org/10.1007/s10543-006-0054-3
   Web of Science ®Google Scholar
• Ouannas, A., Khennaoui, A. A., Momani, S., Pham, V. T., & El-Khazali, R. (2020). Hidden attractors in a new fractional–order discrete system: Chaos, complexity, entropy, and control. Chinese Physics B, 29(5), Article number: 050504. https://doi.org/10.1088/1674-1056/ab820d
   PubMed Web of Science ®Google Scholar
• Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821–824. https://doi.org/10.1103/PhysRevLett.64.821
   PubMed Web of Science ®Google Scholar
• Peng, D. X., Li, J. X., Xu, W., & Li, X. D. (2020). Finite-time synchronization of coupled Cohen–Grossberg neural networks with mixed time delays. Journal of the Franklin Institute, 357(16), 11349–11367. https://doi.org/10.1016/j.jfranklin.2019.06.025
   Web of Science ®Google Scholar
• Podlubny, I. (1999). Fractional differential equations. Academic Press.
   Google Scholar
• Qu, H. Z., Zhang, T. W., & Zhou, J. W. (2020). Global stability analysis of S-asymptotically ω-periodic oscillation in fractional-order cellular neural networks with time variable delays. Neurocomputing, 399, 390–398. https://doi.org/10.1016/j.neucom.2020.03.005
   Web of Science ®Google Scholar
• Sharma, R., Bhasin, S., Gaur, P., & Joshi, D. (2019). A switching-based collaborative fractional order fuzzy logic controllers for robotic manipulators. Applied Mathematical Modelling, 73(3), 228–246. https://doi.org/10.1016/j.apm.2019.03.041
   Web of Science ®Google Scholar
• Sharma, R. K., Xiong, X., Kamal, S., & Ghosh, S. (2021). Discrete-time super-twisting fractional-order differentiator with implicit euler method. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(4), 1238–1242. https://doi.org/10.1109/TCSII.2020.3027733
   Web of Science ®Google Scholar
• Shi, Y. C., & Cao, J. D. (2020). Finite-time synchronization of memristive Cohen–Grossberg neural networks with time delays. Neurocomputing, 377(5), 159–167. https://doi.org/10.1016/j.neucom.2019.10.036
   Web of Science ®Google Scholar
• Stamov, G., Stamova, I., Martynyuk, A., & Stamov, T. (2021). Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives. Chaos, Solitons & Fractals, 143(1), Article number: 110647. https://doi.org/10.1016/j.chaos.2020.110647
   Web of Science ®Google Scholar
• Stamova, I., Stamov, G., Simeonov, S., & Ivanov, A. (2018). Mittag–Leffler stability of impulsive fractional-order bi-directional associative memory neural networks with time-varying delays. Transactions of the Institute of Measurement and Control, 40(10), 3068–3077. https://doi.org/10.1177/0142331217714306
   Web of Science ®Google Scholar
• Wang, J. R., Fekan, M., & Zhou, Y. (2013). Presentation of solutions of impulsive fractional Langevin equations and existence results. The European Physical Journal Special Topics, 222(8), 1857–1874. https://doi.org/10.1140/epjst/e2013-01969-9
   Web of Science ®Google Scholar
• Wang, X. M., & Dong, X. G. (2010). A concise tutorial on computational methods. Science Press.
   Google Scholar
• Wu, G. C., Abdeljawad, T., Liu, J. L., Baleanu, D., & Wu, K. T. (2019). Mittag–Leffler stability analysis of fractional discrete-time neural networks via fixed point technique. Nonlinear Analysis: Modelling and Control, 24(6), 919–936. https://doi.org/10.15388/NA.2019.6.5
   Web of Science ®Google Scholar
• Wu, G. C., Deng, Z. G., Baleanu, D., & Zeng, D. Q. (2019). New variable-order fractional chaotic systems for fast image encryption, Chaos, 29(8), Article number: 083103. https://doi.org/10.1063/1.5096645
   Web of Science ®Google Scholar
• Wu, G. C., Zeng, D. Q., & Baleanu, D. (2019). Fractional impulsive differential equations: Exact solutions, integral equations and short memory case. Fractional Calculus and Applied Analysis, 22(1), 180–192. https://doi.org/10.1515/fca-2019-0012
   Web of Science ®Google Scholar
• Xiao, M., Zheng, W. X., Jiang, G. P., & Cao, J. D. (2015). Undamped oscillations generated by Hopf bifurcations in fractional-order neural networks with Caputo derivative. IEEE Transactions on Neural Networks and Learning Systems, 26(12), 3201–3214. https://doi.org/10.1109/TNNLS.2015.2425734
   PubMed Web of Science ®Google Scholar
• Yang, T., & Yang, L. B. (1996). The global stability of fuzzy cellular neural networks. IEEE Transactions on Circuits and Systems I, 43(10), 880–883. https://doi.org/10.1109/81.538999
   Google Scholar
• Yang, Z. W., Zheng, X. C., Zhang, Z. Q., & Wang, H. (2021). Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise. Chaos, Solitons and Fractals, 142, Article number: 110392. https://doi.org/10.1016/j.chaos.2020.110392
   Web of Science ®Google Scholar
• You, X. X., Song, Q. K., & Zhao, Z. J. (2020). Global Mittag–Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay. Neural Networks, 122(232), 382–394. https://doi.org/10.1016/j.neunet.2019.11.004
   PubMed Web of Science ®Google Scholar
• Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
   Google Scholar
• Zhang, G. D., Zeng, Z. G., & Ning, D. (2020). Novel results on synchronization for a class of switched inertial neural networks with distributed delays. Information Sciences, 511(1), 114–126. https://doi.org/10.1016/j.ins.2019.09.048
   Web of Science ®Google Scholar
• Zhang, Q. H., Yang, L. H., & Liu, J. Z. (2014). Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen–Grossberg neural networks on time scales. Mathematica Slovaca, 64(1), 119–138. https://doi.org/10.2478/s12175-013-0191-5
   Web of Science ®Google Scholar
• Zhang, T. W., Han, S. F., & Zhou, J. W. (2020). Dynamic behaviours for semi-discrete stochastic Cohen–Grossberg neural networks with time delays. Journal of the Franklin Institute, 357(17), 13006–13040. https://doi.org/10.1016/j.jfranklin.2020.09.006
   Web of Science ®Google Scholar
• Zhang, T. W., & Li, Y. K. (2022a). S-asymptotically periodic fractional functional differential equations with off-diagonal matrix Mittag–Leffler function kernels. Mathematics and Computers in Simulation, 193, 331–347. https://doi.org/10.1016/j.matcom.2021.10.006
   Web of Science ®Google Scholar
• Zhang, T. W., & Li, Y. K. (2022b). Exponential Euler scheme of multi-delay Caputo–Fabrizio fractional-order differential equations. Applied Mathematics Letters, 124, Article number: 107709. https://doi.org/10.1016/j.aml.2021.107709
   Web of Science ®Google Scholar
• Zhang, T. W., & Xiong, L. L. (2020). Periodic motion for impulsive fractional functional differential equations with piecewise Caputo derivative. Applied Mathematics Letters, 101, Article number: 106072. https://doi.org/10.1016/j.aml.2019.106072
   Web of Science ®Google Scholar
• Zhang, T. W., Zhou, J. W., & Liao, Y. Z.. (in press). Exponentially stable periodic oscillation and Mittag–Leffler stabilization for fractional-order impulsive control neural networks with piecewise Caputo derivatives. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2021.3054946
   Web of Science ®Google Scholar
• Zheng, M. W., Li, L. X., Peng, H. P., Xiao, J. H., Yang, Y. X., Y. P. Zhang, & Zhao, H. (2018). Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks. Communications in Nonlinear Science and Numerical Simulation, 59(10), 272–291. https://doi.org/10.1016/j.cnsns.2017.11.025
   Web of Science ®Google Scholar