Abstract
This paper focuses on the global asymptotic stability of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time delays. By virtue of homeomorphism theory, inequality techniques and Lyapunov functional, a set of delay-independent sufficient conditions is established for assuring the existence, uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model. The assumption on boundedness of the activation functions is not required, and the LMI-based criteria are easy to be checked and executed in practice. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.
Similar content being viewed by others
References
Hirose, A.: Recent progress in applications of complex-valued neural networks. In: Rutkowski, L., et al. (eds.) Artificial Intelligence and Soft Computing (ICAISC2010). Part II, Lecture Notes in Artificial Intelligence, vol. 6114, pp. 42–46. Springer, New York (2010)
Hirose, A.: Complex-valued neural networks: theories and applications. In: Jain, L.C. (eds.) Series on Innovative Intelligence, vol. 5. World Scientific, Singapore (2003)
Hu, J., Wang, J.: Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans. Neural Netw. Learn. Syst. 23(6), 853–865 (2012)
Arbi, A., Aouiti, C., Cherif, F., Touati, A., Alimi, A.M.: Stability analysis for delayed high-order type of Hopfield neural networks with impulses. Neurocomputing 165, 312–329 (2015)
Fang, T., Sun, J.T.: Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans. Neural Netw. Learn. Syst. 25(9), 1709–1713 (2014)
Hien, L.V.: On global exponential stability of positive neural networks with time-varying delay. Neural Netw. 87, 22–26 (2017)
Song, Q.K., Zhao, Z.J.: Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171, 179–184 (2016)
Lee, W.I., Lee, S.Y., Park, P.: Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functionals. Neurocomputing 155, 128–134 (2015)
Zhang, Z.Y., Lin, C., Chen, B.: Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(9), 1704–1708 (2014)
Singh, J., Barabanov, N.: Stability of discrete time recurrent neural networks and nonlinear optimization problems. Neural Netw. 74, 58–72 (2015)
Xie, D., Jiang, Y.P.: Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 207, 528–538 (2016)
Balasundaram, K., Raja, R., Zhu, Q.X., Chandrasekaran, S., Zhou, H.W.: New global asymptotic stability of discrete-time recurrent neural networks with multiple time-varying delays in the leakage term and impulsive effects. Neurocomputing 214, 420–429 (2016)
Tan, M.C., Zhang, Y.N.: New sufficient conditions for global asymptotic stability of Cohen–Grossberg neural networks with time-varying delays. Nonlinear Anal. 10, 2139–2145 (2009)
Samli, R., Yucel, E.: Global robust stability analysis of uncertain neural networks with time varying delays. Neurocomputing 167, 371–377 (2015)
Gong, W.Q., Liang, J.L., Zhang, C.J., Cao, J.D.: Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process. Lett. 44(2), 539–554 (2015)
Velmurugana, G., Rakkiyappan, R., Cao, J.D.: Further analysis of global \(\mu \)-stability of complex-valued neural networks with unbounded time-varying delays. Neural Netw. 67, 14–27 (2015)
Song, Q.K., Yan, H., Zhao, Z.J., Liu, Y.R.: Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw. 81, 1–10 (2016)
Tan, M.C.: Global asymptotic stability of fuzzy cellular neural networks with unbounded distributed delays. Neural Process. Lett. 31(2), 147–157 (2010)
Muthukumar, P., Subramanian, K.: Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination. Neurocomputing 205, 75–83 (2016)
Zhang, Z.Q., Yu, S.H.: Global asymptotic stability for a class of complex-valued Cohen–Grossberg neural networks with time delays. Neurocomputing 171, 1158–1166 (2016)
Zeng, X., Li, C.D., Huang, T.W., He, X.: Stability analysis of complex-valued impulsive systems with time delay. Appl. Math. Comput. 256, 75–82 (2015)
Berezansky, L., Braverman, E., Idels, L.: New global exponential stability criteria for nonlinear delay differential systems with applications to BAM neural networks. Appl. Math. Comput. 243, 899–910 (2014)
Xu, X.H., Zhang, J.Y., Shi, J.Z.: Exponential stability of complex-valued neural networks with mixed delays. Neurocomputing 128, 483–490 (2014)
Gong, W.Q., Liang, J.L., Cao, J.D.: Global \(\mu \)-stability of complex-valued delayed neural networks with leakage delay. Neurocomputing 168, 135–144 (2015)
Pan, J., Liu, X.Z., Xie, W.C.: Exponential stability of a class of complex-valued neural networks with time-varying delays. Neurocomputing 164, 293–299 (2015)
Stamova, I.: Global Mittag–Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays. Nonlinear Dyn. 77, 1251–1260 (2014)
Song, Q.K., Zhao, Z.J., Liu, Y.R.: Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159, 96–104 (2015)
Tan, M.C.: Stabilization of coupled time-delay neural networks with nodes of different dimensions. Neural Process. Lett. 43(1), 255–268 (2016)
Wang, Z.Y., Huang, L.H.: Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173, 2083–2089 (2016)
Dong, T., Liao, X.F., Wang, A.J.: Stability and Hopf bifurcation of a complex-valued neural network with two time delays. Nonlinear Dyn. 82(1–2), 173–184 (2015)
Ma, J., Song, X.L., Jin, W.Y., Wang, C.N.: Autapse-induced synchronization in a coupled neuronal network. Chaos Solitons Fract. 80, 31–38 (2015)
Song, X.L., Wang, C.N., Ma, J., Ren, G.D.: Collapse of ordered spatial pattern in neuronal network. Phys. A 451, 95–112 (2016)
Ma, J., Xu, Y., Ren, G.D., Wang, C.N.: Prediction for breakup of spiral wave in a regular neuronal network. Nonlinear Dyn. 84(2), 497–509 (2016)
Weera, W., Niamsup, P.: Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays. Neurocomputing 173, 921–929 (2016)
Wang, X.H., Li, S.Y., Xu, D.Y.: Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nolinear Dyn. 64, 65–75 (2015)
Peng, W.L., Wu, Q.X., Zhang, Z.Q.: LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique. Neurocomputing 199, 103–113 (2016)
Senthilraj, S., Raja, R., Jiang, F., Zhu, Q.X., Samidurai, R.: New delay-interval-dependent stability analysis of neutral type BAM neural networks with successive time delay components. Neurocomputing 171, 1265–1280 (2016)
Zhang, Z.Q., Liu, K.Y., Yang, Y.: New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81, 24–32 (2012)
Sayli, M., Yilmaz, E.: Global robust asymptotic stability of variable-time impulsive BAM neural networks. Neural Netw. 60, 67–73 (2014)
Forti, M., Tesi, A.: New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I(42), 354–366 (1995)
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnam, V.: Linear Matrix Inequality in System and Control Theory. SIAM, Philadelphia (1994)
Acknowledgements
The research is supported by Grants from the National Natural Science Foundation of China (Nos. 61572233 and 11471083) and the Science and Technology Program of Guangzhou, China (No. 201707010404).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, D., Tan, M. Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays. Nonlinear Dyn 89, 819–832 (2017). https://doi.org/10.1007/s11071-017-3486-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-017-3486-1