Abstract
In this paper, a nonautonomous impulsive neutral-type neural network with delays is considered. By establishing a singular impulsive delay differential inequality and employing contraction mapping principle, several sufficient conditions ensuring the existence and global exponential stability of the periodic solution for the impulsive neutral-type neural network with delays are obtained. Our results can extend and improve earlier publications. An example is given to illustrate the theory.
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References
Zhao, H.: Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Appl. Math. Comput. 154, 683–695 (2004)
Zhao, H.: Global exponential stability and periodicity of cellular neural networks with variable delays. Phys. Lett. A 336, 331–341 (2005)
Zhao, H., Chen, L., Mao, Z.: Existence and stability of almost periodic solution for Cohen-Grossberg neural networks with variable coefficients. Nonlinear Anal. 9, 663–673 (2008)
Huang, X., Cao, J., Daniel, W.C.: Existence and attractivity of almost periodic solution for recurrent neural networks with unbounded delays and variable coefficients. Nonlinear Dyn. 45, 337–351 (2006)
Wang, L., Gao, Y.: Global exponential robust stability of reaction-diffusion interval neural networks with S-type distributed time-varying delays. Phys. Lett. A 5–6, 342–348 (2006)
Wang, L., Cao, J.: Global robust point dissipativity of interval neural networks with mixed time-varying delays. Nonlinear Dyn. 55, 169–178 (2009)
Wang, L., Zhang, R., Wang, Y.: Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays. Nonlinear Anal. 10, 1101–1113 (2009)
Qiu, J., Cao, J.: Delay-dependent robust stability of neutral-type neural networks with time delays. J. Math. Cont. Sci. Appl. 1, 179–188 (2007)
Cao, J., Zhong, S., Hu, Y.: Global stability analysis for a class of neural networks with time varying delays and control input. Appl. Math. Comput. 189, 1480–1490 (2007)
Bai, C.: Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays. Appl. Math. Comput. 203, 72–79 (2008)
Gui, Z., Ge, W., Yang, X.: Periodic oscillation for a Hopfield neural networks with neutral delays. Phys. Lett. A 364, 267–273 (2007)
Park, J.H., Kwon, O.M., Lee, S.M.: LMI optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196, 236–244 (2008)
Park, J.H., Kwon, O.M., Lee, S.M.: State estimation for neural networks of neutral-type with interval time-varying delay. Appl. Math. Comput. 203, 217–223 (2008)
Park, J.H., Park, C.H., Kwon, O.M., Lee, S.M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199, 716–722 (2008)
Park, J.H., Kwon, O.M.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202, 360–369 (2008)
Rakkiyappan, R., Balasubramaniam, P.: New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71, 1039–1045 (2008)
Rakkiyappan, R., Balasubramaniam, P.: LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl. Math. Comput. 204, 317–324 (2008)
Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
Arbib, M.: Branins, Machines, and Mathematics. Springer, New York (1987)
Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs, New Jersey (1998)
Xu, D., Yang, Z.: Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, 107–120 (2005)
Yang, Z., Xu, D.: Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays. Appl. Math. Comput. 177, 63–78 (2006)
Yang, Z., Xu, D.: Existence and exponential stability of periodic solution for impulsive delay differential equations and applications. Nonlinear Anal. 64, 130–145 (2006)
Xu, D., Yang, Z., Yang, Z.: Exponential stability of nonlinear impulsive neutral differential equations with delays. Nonlinear Anal. 67, 1426–1439 (2007)
Weng, A., Sun, J.: Globally exponential stability of periodic solutions for nonlinear impulsive delay systems. Nonlinear Anal. 67, 1938–1946 (2007)
Xia, Y., Cao, J., Cheng, S.: Global exponential stability of delayed cellular neural networks with impulses. Neurocomputing 70, 2495–2501 (2007)
Yang, Y., Cao, J.: Stability and periodicity in delayed cellular neural networks with impulsive effects. Nonlinear Anal. 7, 362–374 (2007)
Wang, Q., Liu, X.: Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals. Appl. Math. Comput. 194, 86–198 (2007)
Gui, Z., Yang, X., Ge, W.: Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays. Math. Comput. Simul. 79, 14–29 (2008)
Benchohra, M., Ouahabi, A.: Some uniqueness results for impulsive semilinear neutral functional differential equations. Georgian Math. J. 9, 423–430 (2002)
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Wang, X., Li, S. & Xu, D. Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dyn 64, 65–75 (2011). https://doi.org/10.1007/s11071-010-9846-8
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DOI: https://doi.org/10.1007/s11071-010-9846-8