Multiple asymptotical stability analysis for fractional-order neural networks with time delays

References

• Balasubramaniam, P., & Vidhya, C. (2012). Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters. Expert Systems with Applications, 39(3), 3109–3115. doi: 10.1016/j.eswa.2011.08.174
   Web of Science ®Google Scholar
• Bao, H. B., Park, J. H., & Cao, J. (2015). Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dynamics, 82, 1343–1354. doi: 10.1007/s11071-015-2242-7
   Web of Science ®Google Scholar
• Cao, J., & Wang, J. (2005). Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Transactions on Circuits and Systems I: Regular Papers, 52(2), 417–426. doi: 10.1109/TCSI.2004.841574
   Web of Science ®Google Scholar
• Chen, L. P., Chai, Y., Wu, R. C., Ma, T. D., & Zhai, H. Z. (2013). Dynamic analysis of a case of fractional-order neural networks with delay. Neurocomputing, 111(2), 190–194. doi: 10.1016/j.neucom.2012.11.034
   Web of Science ®Google Scholar
• Chen, B. S., & Chen, J. J. (2015). Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks. Neural Networks, 68, 78–88. doi: 10.1016/j.neunet.2015.04.006
   PubMed Web of Science ®Google Scholar
• Chen, B. S., & Chen, J. J. (2016). Global O(t−α) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays. Neural Networks, 73, 47–57. doi: 10.1016/j.neunet.2015.09.007
   PubMed Web of Science ®Google Scholar
• Chen, B. S., & Wang, J. (2005). Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. IEEE Transactions on Neural Networks, 16, 1440–1448. doi: 10.1109/TNN.2005.857953
   PubMed Web of Science ®Google Scholar
• Chen, B. S., & Wang, J. (2007). Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays. Neural Networks, 20(10), 1067–1080. doi: 10.1016/j.neunet.2007.07.007
   PubMed Web of Science ®Google Scholar
• Chen, J. J., Zeng, Z. G., & Jiang, P. (2014a). Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Networks, 51, 1–8. doi: 10.1016/j.neunet.2013.11.016
   PubMed Web of Science ®Google Scholar
• Chen, J. J., Zeng, Z. G., & Jiang, P. (2014b). On the periodic dynamics of memristor-based neural networks with time-varying delays. Information Sciences, 279, 358–373. doi: 10.1016/j.ins.2014.03.124
   Web of Science ®Google Scholar
• Chen, W.-H., & Zheng, W. X. (2010). Robust stability analysis for stochastic neural networks with time-varying delay. IEEE Transactions on Neural Networks, 21(3), 508–514. doi: 10.1109/TNN.2009.2040000
   PubMed Web of Science ®Google Scholar
• Deng, W. H., Li, C. P., & Lü, J. H. (2007). Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics, 48(4), 409–416. doi: 10.1007/s11071-006-9094-0
   Web of Science ®Google Scholar
• Halanay, A. (1966). Differential equations (pp. 378–378). New York: Academic Press.
   Google Scholar
• He, Y., Liu, G. P., Rees, D., & Wu, M. (2007). Stability analysis for neural networks with time-varying interval delay. IEEE Transactions on Neural Networks, 18(6), 1850–1854. doi: 10.1109/TNN.2007.903147
   Web of Science ®Google Scholar
• He, Y., Liu, G. P., & Rees, D. (2007). New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Transactions on Neural Networks, 18(1), 310–314. doi: 10.1109/TNN.2006.888373
   PubMed Web of Science ®Google Scholar
• Hu, C., Jiang, H. J., & Teng, Z. D. (2010). Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms. IEEE Transactions on Neural Networks, 21(1), 67–81. doi: 10.1109/TNN.2009.2034318
   PubMed Web of Science ®Google Scholar
• Huang, H., Huang, T. W., & Chen, X. P. (2013). A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Networks, 46, 50–61. doi: 10.1016/j.neunet.2013.04.014
   PubMed Web of Science ®Google Scholar
• Huang, X., Zhao, Z., Wang, Z., & Li, Y. X. (2012). Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing, 94, 13–21. doi: 10.1016/j.neucom.2012.01.011
   Web of Science ®Google Scholar
• Jiang, H. J., & Teng, Z. D. (2004). Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Networks, 17(10), 1415–1425. doi: 10.1016/j.neunet.2004.03.002
   PubMed Web of Science ®Google Scholar
• Kaslik, E., & Sivasundaram, S. (2012). Dynamics of fractional-order neural networks. 2010 International joint conference on neural networks, IJCNN 2010 (pp. 611–618). San Jose.
   Google Scholar
• Li, Y., Chen, Y., & Podlubny, I. (2009). Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45(8), 1965–1969. doi: 10.1016/j.automatica.2009.04.003
   Web of Science ®Google Scholar
• Liang, S., Wu, R. C., & Chen, L. P. (2015). Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays. Neurocomputing, 168, 618–625. doi: 10.1016/j.neucom.2015.05.063
   Web of Science ®Google Scholar
• Liu, Y. R., Wang, Z. D., & Liu, X. H. (2006). Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks, 19(5), 667–675. doi: 10.1016/j.neunet.2005.03.015
   PubMed Web of Science ®Google Scholar
• Liu, P., Zeng, Z. G., & Wang, J. (2016a). Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays. Neural Networks, 79, 117–127. doi: 10.1016/j.neunet.2016.03.010
   PubMed Web of Science ®Google Scholar
• Liu, P., Zeng, Z. G., & Wang, J. (2016b). Multistability of recurrent neural networks with nonmonotonic activation functions and mixed delays. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 46(4), 512–523. doi: 10.1109/TSMC.2015.2461191
   Web of Science ®Google Scholar
• Liu, P., Zeng, Z. G., & Wang, J. (2017). Multiple Mittag–Leffler stability of fractional-order recurrent neural networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 2279–2288. doi: 10.1109/TSMC.2017.2651059
   Web of Science ®Google Scholar
• Nie, X., & Cao, J. (2009). Multistability of competitive neural networks with time-varying and distributed delays. Nonlinear Analysis: Real World Applications, 10(2), 928–942. doi: 10.1016/j.nonrwa.2007.11.014
   Web of Science ®Google Scholar
• Song, L., Wu, R. C., & Chen, L. P. (2015). Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays. Neurocomputing, 168, 618–625. doi: 10.1016/j.neucom.2015.05.020
   Web of Science ®Google Scholar
• Song, Q. K., Yan, H., Zhao, Z. J., & Liu, Y. R. (2016). Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Networks, 81, 1–10. doi: 10.1016/j.neunet.2016.04.012
   PubMed Web of Science ®Google Scholar
• Wan, L. G., & Wu, A. L. (2018). Multistability in Mittag–Leffler sense of fractional-order neural networks with piecewise constant arguments. Neurocomputing, 286, 1–10. doi: 10.1016/j.neucom.2018.01.049
   Web of Science ®Google Scholar
• Wang, L. L., & Chen, T. P. (2014). Multiple μ-stability of neural networks with unbounded time-varying delays. Neural Networks, 53, 109–118. doi: 10.1016/j.neunet.2014.02.001
   PubMed Web of Science ®Google Scholar
• Wang, D., & Huang, L. (2014). Periodicity and global exponential stability of generalized Cohen–Grossberg neural networks with discontinuous activations and mixed delays. Neural Networks, 51, 80–95. doi: 10.1016/j.neunet.2013.12.005
   PubMed Web of Science ®Google Scholar
• Wang, Z. D., Liu, Y. R., Li, M. Z., & Liu, X. H. (2006). Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks, 17(3), 814–820. doi: 10.1109/TNN.2006.872355
   PubMed Web of Science ®Google Scholar
• Wang, L. L., Lu, W. L., & Chen, T. P. (2009). Multistability and new attraction basins of almost-periodic solutions of delayed neural networks. IEEE Transactions on Neural Networks, 20(10), 1581–1593. doi: 10.1109/TNN.2009.2027121
   PubMed Web of Science ®Google Scholar
• Wang, L. L., Lu, W. L., & Chen, T. P. (2010). Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions. Neural Networks, 23(2), 189–200. doi: 10.1016/j.neunet.2009.11.010
   PubMed Web of Science ®Google Scholar
• Wang, F., Yang, Y. Q., & Hu, M. F. (2015). Asymptotic stability of delayed fractional-order neural networks with impulsive effects. Neurocomputing, 154, 239–244. doi: 10.1016/j.neucom.2014.11.068
   Web of Science ®Google Scholar
• Wang, H., Yu, Y. G., Wen, G. G., & Zhang, S. (2015). Stability analysis of fractional-order neural Networks with time delay. Neural Processing Letters, 42(2), 479–500. doi: 10.1007/s11063-014-9368-3
   Web of Science ®Google Scholar
• Wang, H., Yu, Y. G., Wen, G. G., Zhang, S., & Yu, J. Z. (2015). Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing, 154, 15–23. doi: 10.1016/j.neucom.2014.12.031
   Web of Science ®Google Scholar
• Wu, A. L., & Zeng, Z. G. (2016). Boundedness, Mittag–Leffler stability and asymptotical ω-periodicity of fractional-order fuzzy neural networks. Neural Networks, 74, 73–84. doi: 10.1016/j.neunet.2015.11.003
   PubMed Web of Science ®Google Scholar
• Zeng, H. B., He, Y., Wu, M., & Xiao, H. Q. (2014). Improved conditions for passivity of neural networks with a time-varying delay. IEEE Transaction on Cybernetics, 44(6), 785–792. doi: 10.1109/TCYB.2013.2272399
   PubMed Web of Science ®Google Scholar
• Zeng, H. B., Teo, K. L., He, Y., Xu, H. L., & Wang, W. (2017). Sampled-data synchronization control for chaotic neural networks subject to actuator saturation. Neurocomputing, 260, 25–31. doi: 10.1016/j.neucom.2017.02.063
   Web of Science ®Google Scholar
• Zeng, Z. G., & Zheng, W. X. (2013). Multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plane. IEEE Transactions on Neural Networks and Learning Systems, 24(11), 1749–1762. doi: 10.1109/TNNLS.2013.2262638
   PubMed Web of Science ®Google Scholar
• Zhang, H. G., Wang, Z. S., & Liu, D. R. (2008). Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Transactions on Neural Networks, 19(5), 855–873. doi: 10.1109/TNN.2007.912319
   PubMed Web of Science ®Google Scholar
• Zhang, H. G., Wang, Z. S., & Liu, D. R. (2014). A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Transactions on Neural Networks and Learning Systems, 25(7), 1229–1262. doi: 10.1109/TNNLS.2014.2317880
   Web of Science ®Google Scholar
• Zhang, S., Yu, Y. G., & Wang, H. (2015). Mittag-Leffler stability of fractional-order Hopfield neural networks. Nonlinear Analysis: Hybrid Systems, 16, 104–121.
   Web of Science ®Google Scholar
• Zhou, S. B., Li, H., & Zhu, Z. Z. (2008). Chaos control and synchronization in a fractional neuron network system. Chaos, Solitons and Fractals, 36(4), 973–984. doi: 10.1016/j.chaos.2006.07.033
   Web of Science ®Google Scholar