Dissipativity Analysis of Memristor-Based Fractional-Order Hybrid BAM Neural Networks with Time Delays

References

[1] B. Kosko, Bi-directional associative memory, IEEE Trans. Syst. Man Cybern. SMC-18 (1988), 49–60.10.1109/21.87054Suche in Google Scholar

[2] B. Kosko, Adaptive bidirectional associative memories, Appl. Opt. 26 (1989), 4947–4960.10.1364/AO.26.004947Suche in Google Scholar PubMed

[3] B. Kosko, Unsupervised learning in noise. IEEE Trans. Neural Netw. NN-1 (1990), 44–57.10.1109/72.80204Suche in Google Scholar PubMed

[4] B. Kosko, Structural stability of unsupervised learning in feedback neural networks. IEEE Trans. Autom. Control AC-36 (1991), 785–790.10.1109/9.85058Suche in Google Scholar

[5] B. Kosko, Neural networks and fuzzy systems a dynamical system approach to machine intelligence, Englewood Cliffs, NJ, Prentice-Hall, 1992.Suche in Google Scholar

[6] C. Mathai and B. C. Upadhyaya, Performance analysis and application of the bidirectional associative memory to industrial spectral signatures, Proc. IJCNN 1 (1989), 33–37.10.1109/IJCNN.1989.118556Suche in Google Scholar

[7] I. Elsen, K. F. Kraiss and D. Krumbiegel, Pixel based 3D object recognition with bidirection associative memories. Int. Conf. Neural Netw. 3 (1997), 1679–1684.Suche in Google Scholar

[8] B. Maundy and E. I. EI-Masry, A switched capacitor bidirectional associative memory. IEEE Trans. Circ. Syst. 37(12) (1990), 1568–1572.10.1109/31.101281Suche in Google Scholar

[9] S. M. R. Hasan and N. K. Siong, A VLSI BAM neural network chip for pattern recognition applications. Proc. IEEE Int. Conf. Neural Netw. 1 (1995), 164–168.Suche in Google Scholar

[10] J. Zhang and Y. Yang, Global stability analysis of bidirectional associative memory neural networks with time delay. Int. J. Circ. Theor. Appl. 29 (2001), 185–196.10.1002/cta.144Suche in Google Scholar

[11] X. Liao, J. Yu and G. Chen, Novel stability criteria for bidirectional associative memory neural networks with time delays. Int. J. Circ. Theor. Appl. 30 (2002), 519–546.10.1002/cta.206Suche in Google Scholar

[12] Q. Zhou, Global exponential stability of BAM neural networks with distributed delays and impulses. Nonlin. Anal. Real World Appl. 10 (2009), 144–153.10.1016/j.nonrwa.2007.08.019Suche in Google Scholar

[13] X. Liao and K. Wong, Robust stability of interval bidirectional associative memory neural network with time delays. IEEE Trans Syst. Man Cybern. B: Cybern. 34(2) (2004), 1142–1154.10.1109/TSMCB.2003.821455Suche in Google Scholar

[14] Y. Li, Global exponential stability of BAM neural networks with delays and impulses. Chaos Solitons Fractals 24 (2005), 279–285.10.1016/S0960-0779(04)00561-2Suche in Google Scholar

[15] J. Liang and J. Cao, Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. Chaos Solitons Fractals 22 (2004), 773–785.10.1016/j.chaos.2004.03.004Suche in Google Scholar

[16] S. Senan and S. Arik, Global robust stability of bidirectional associative memory neural networks with multiple time delays. IEEE Trans. Syst. Man Cybern. B: Cybern. 37(5) (2007).10.1109/TSMCB.2007.902244Suche in Google Scholar

[17] Q. Song and J. Cao, Global exponential stability of bidirectional associative memory neural networks with distributed delays. J. Comput. Appl. Math. 202 (2007), 266–279.10.1016/j.cam.2006.02.031Suche in Google Scholar

[18] X. Liao and K. Wong, Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays. Phys. Rev. E. 67 (2003), 042901.10.1103/PhysRevE.67.042901Suche in Google Scholar PubMed

[19] S. Arik, Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays. Phys. Lett. A. 351 (2006), 85–91.10.1016/j.physleta.2005.10.059Suche in Google Scholar

[20] L. Wang, L. Zhang and X. Ding, Global dissipativity of a class of BAM neural networks with both time-varying and continuously distributed delays. Neurocomputing 152 (2015), 250–260.10.1016/j.neucom.2014.10.070Suche in Google Scholar

[21] L. Chua, Memristor The Missing Circuit Element. IEEE Trans. Circ. Theory 18(5) (1971), 507–519.10.1109/TCT.1971.1083337Suche in Google Scholar

[22] D. Strukov, G. Snider, D. Stewart and R. Williams, The missing memristor found. Nature 453 (2008), 80–83.10.1038/nature06932Suche in Google Scholar

[23] J. Tour and T. He, The fourth element. Nature 453 (2008), 42–43.10.1038/453042aSuche in Google Scholar

[24] S. Adhikari, C. Yang, H. Kim and L. Chua, Memristor bridge synapse-based neural network and its learning. IEEE Trans. Neural Netw. Learn. Syst. 23(9) (2012), 1426–1435.10.1109/TNNLS.2012.2204770Suche in Google Scholar PubMed

[25] S. Duan, X. Hu, Z. Dong, L. Wang and P. Mazumder, Memristor-based cellular nonlinear neural network: design, analysis, and applications. IEEE Trans. Neural Netw. Learn. 26(6) (2014), 1202–1213.10.1109/TNNLS.2014.2334701Suche in Google Scholar PubMed

[26] Y. Pershin, M. Ventra, Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23(7) (2010), 881–886.10.1016/j.neunet.2010.05.001Suche in Google Scholar PubMed

[27] Z. Cai and L. Huang, Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays. Commun. Nonlin. Sci. Numer. Simul. 19 (2014), 1279–1300.10.1016/j.cnsns.2013.09.004Suche in Google Scholar

[28] H. Li, H. Jiang and C. Hu, Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays. Neural Netw. 75 (2016), 97–109.10.1016/j.neunet.2015.12.006Suche in Google Scholar

[29] R. Guo, Z. Zhang, X. Liu and C. Lin, Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays. Appl. Math. Comput. 311 (2017), 100–117.10.1016/j.amc.2017.05.021Suche in Google Scholar

[30] R. Guo, Z. Zhang, X. Liu, C. Lin, H. Wang and J. Chen, Exponential input-to-state stability for complex-valued memristor-based BAM neural networks with multiple time-varying delays. Neurocomputing 275 (2018), 2041–2054.10.1016/j.neucom.2017.10.038Suche in Google Scholar

[31] A. Carpinteri, P. Cornetti and K. Kolwankar, Calculation of the tensile and flexural strength of disordered materials using fractional calculus. Chaos Solitons Fractals 21 (2004), 623–632.10.1016/j.chaos.2003.12.081Suche in Google Scholar

[32] S. Das, D. Tripathi and S. Pandey, Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel. Appl. Math. Comput. 215 (2010), 3645–3654.10.1016/j.amc.2009.11.002Suche in Google Scholar

[33] A. Gokdogan, M. Merdan and A. Yildirim, A multistage differential transformation method for approximate solution of Hantavirus infection model. Commun. Nonlin. Sci. Numer. Simul. 17 (2012), 1–8.10.1016/j.cnsns.2011.05.023Suche in Google Scholar

[34] V. Kulish and J. Lage, Application of fractional calculus to fluid mechanics. J. Fluids Eng. 124 (2002), 803–806.10.1115/1.1478062Suche in Google Scholar

[35] B. Lundstrom, M. Higgs, W. Spain and A. Fairhall, Fractional differentiation by neocortical pyramidal neurons. Nat. Neurosci. 11 (2008), 1335–1342.10.1038/nn.2212Suche in Google Scholar

[36] R. Magin, Fractional calculus in bioengineering, part 3. Crit. Rev. Biomed. Eng. 32 (2004), 195–377.10.1615/CritRevBiomedEng.v32.i34.10Suche in Google Scholar

[37] R. Magin, Modeling the cardiac tissue electrode interface using fractional calculus. J. Vib. Control 14 (2008), 1431–1442.10.1177/1077546307087439Suche in Google Scholar

[38] R. Magin, Fractional calculus models of complex dynamics in biological tissues. Comput. Math. Appl. 59 (2010), 1585–1593.10.1016/j.camwa.2009.08.039Suche in Google Scholar

[39] E. Soczkiewicz, Application of fractional calculus in the theory of viscoelasticity. Mol. Quant. Acoust. 23 (2002), 397–404.Suche in Google Scholar

[40] J. Sabatier, O. Agrawal and J. Machado, Theoretical developments and applications, Advance in fractional calculus. Springer, Berlin, 2007.10.1007/978-1-4020-6042-7Suche in Google Scholar

[41] A. Yildirim, An algorithm for solving the fractional nonlinear schrodinger equation by means of the homotopy perturbation method. Int. J. Nonlin. Sci. Numer. Simul. 10 (2011), 445–451.10.1515/IJNSNS.2009.10.4.445Suche in Google Scholar

[42] L. Zhang and Y. Yang, Different impulsive effects on synchronization of fractional-order memristive BAM neural networks. Nonlin. Dyn. https://doi.org/10.1007/s11071-018-4188-z.Suche in Google Scholar

[43] J. Xiao, S. Zhong, Y. Li, et al., Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays. Neurocomputing 219 (2017), 431–439.10.1016/j.neucom.2016.09.049Suche in Google Scholar

[44] I. Podlubny, Fractional differential equations, Academic Press, New York, 1999.Suche in Google Scholar

[45] A. F. Filippov, Differential equations with discontinuous righthand sides, Kluwer Academic, Boston, 1988.10.1007/978-94-015-7793-9Suche in Google Scholar

[46] Z. Ding and Y. Shen, Global dissipativity of fractional-order neural networks with time delays and discontinuous activations. Neurocomputing 196 (2016), 159-166.10.1016/j.neucom.2016.03.005Suche in Google Scholar

[47] J. Chen, Z. Zeng and P. Jiang, Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw. 51 (2014), 1–8.10.1016/j.neunet.2013.11.016Suche in Google Scholar

[48] S. Zhang, Y. Yu and H. Wang, Mittag-Leffler stability of fractional-order Hopfield neural networks. Nonlin. Anal. Hybrid. Syst. 16 (2015), 104–121.10.1016/j.nahs.2014.10.001Suche in Google Scholar

[49] A. Granas and J. Dugundji, Fixed point theory, Springer-Verlag, New York, 2003.10.1007/978-0-387-21593-8Suche in Google Scholar

[50] D. Wang, A. Xiao and H. Liu, Dissipativity and stability analysis for fractional functional differential equations. Fract. Calc. Appl. Anal. 18(6) (2015), 1399–1422.10.1515/fca-2015-0081Suche in Google Scholar

[51] H. Wang, Y. Yu, G. Wen, S. Zhang and J. Yu, Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154 (2015), 15–23.10.1016/j.neucom.2014.12.031Suche in Google Scholar

[52] G. Velmurugan, R. Rakkiyappan, V. Vembarasan, J. Cao and A. Alsaedi, Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay. Neural Netw. 86 (2017), 42–53.10.1016/j.neunet.2016.10.010Suche in Google Scholar

[53] L. Wang, Q. Song, Y. Liu, Z. Zhao and F. Alsaadi, Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay. Neurocomputing 243 (2017), 49–59.10.1016/j.neucom.2017.02.086Suche in Google Scholar