Abstract
In the paper, the problem on the stability of anti-periodic solutions is investigated for high-order neural networks with discrete and distributed time delays. Several sufficient conditions for checking the existence, uniqueness and global exponential stability of anti-periodic solution for the considered neural networks are given. A numerical example is given to show its effectiveness.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Okochi, H.: On the existence of periodic solutions to nonlinear abstract parabolic equations. J. Math. Soc. Japan 40, 541–553 (1988)
Chen, Y.: Anti-periodic solutions for semilinear evolution equations. J. Math. Anal. Appl. 315, 337–348 (2006)
Wu, R.: An anti-periodic LaSalle oscillation theorem. Appl. Math. Lett. 21, 928–933 (2008)
Yin, Y.: Remarks on first order differential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2, 83–94 (1995)
Aizicovici, S., McKibben, M., Reich, S.: Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal. 43, 233–251 (2001)
Chen, Y., Nieton, J.J., O’Regan, D.: Anti-periodic solutions for fully nonlinear first-order differential equations. Math. Comput. Modell. 46, 1183–1190 (2007)
Wang, K., Li, Y.: A note on existence of (anti-)periodic and heteroclinic solutions for a class of second-order odes. Nonlinear Anal. 70, 1711–1724 (2009)
Peng, G., Huang, L.: Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal. Real World Appl. 10, 2434–2440 (2009)
Shao, J.: An anti-periodic solution for a class of recurrent neural networks. J. Comput. Appl. Math. 228, 231–237 (2009)
Delvos, F.J., Knoche, L.: Lacunary interpolation by antiperiodic trigonometric polynomials. BIT Numer. Math. 39, 439–450 (1999)
Du, J., Han, H., Jin, G.: On trigonometric and paratrigonometric Hermite interpolation. J. Approx. Theory 131, 74–99 (2004)
Chen, H.L.: Antiperiodic wavelets. J. Comput. Math. 14, 32–39 (1996)
Zhang, B., Xu, S., Li, Y., Chu, Y.: On global exponential stability of high-order neural networks with time-varying delays. Phys. Lett. A 366, 69–78 (2007)
Lou, X., Cui, B.: Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. J. Math. Anal. Appl. 330, 144–158 (2007)
Ou, C.: Anti-periodic solutions for high-order Hopfield neural networks. Comput. Math. Appl. 56, 1838–1844 (2008)
Huang, Z., Song, Q., Feng, C.: Multistability in networks with self-excitation and high-order synaptic connectivity. IEEE Trans. Circuits Syst. I 57, 2144–2155 (2010)
Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, X., Song, Q. (2011). Anti-periodic Solutions for High-Order Neural Networks with Mixed Time Delays. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-21105-8_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21104-1
Online ISBN: 978-3-642-21105-8
eBook Packages: Computer ScienceComputer Science (R0)