×

Anti-periodic solutions for high-order Hopfield neural networks. (English) Zbl 1152.34378

Summary: In this paper high-order Hopfield neural networks (HHNNs) with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established, which are new and complement previously known results.

MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology
92B20 Neural networks for/in biological studies, artificial life and related topics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Wang, Z.; Fang, J.; Liu, X., Global stability of stochastic high-order neural networks with discrete and distributed delays, Chaos solitons fractals, 36, 2, 388-396, (2008) · Zbl 1141.93416
[2] Mohamad, S., Exponential stability in Hopfield-type neural networks with impulses, Chaos solitons fractals, 32, 2, 456-467, (2007), 81 (1984) 3088-3092 · Zbl 1143.34031
[3] Liu, Y.; You, Z., Multi-stability and almost periodic solutions of a class of recurrent neural networks, Chaos solitons fractals, 33, 2, 554-563, (2007) · Zbl 1136.34311
[4] Y. Jiang, B. Yang, J. Wang, C. Shao, Delay-dependent stability criterion for delayed Hopfield neural networks, Chaos Solitons Fractals, doi:10.1016/j.chaos.2007.06.039 · Zbl 1197.34136
[5] Xiao, B.; Meng, H., Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks, Appl. math. modell., (2007)
[6] Liu, B.; Huang, L., Existence and exponential stability of periodic solutions for a class of cohen – grossberg neural networks with time-varying delays, Chaos solitons fractals, 32, 2, 617-627, (2007) · Zbl 1145.34049
[7] Zhang, F.; Li, Y., Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions, Electron. J. diff. eqns., 2007, 97, 1-10, (2007) · Zbl 1138.34346
[8] Okochi, H., On the existence of periodic solutions to nonlinear abstract parabolic equations, J. math. soc. Japan, 40, 3, 541-553, (1988) · Zbl 0679.35046
[9] Aftabizadeh, A.R.; Aizicovici, S.; Pavel, N.H., On a class of second-order anti-periodic boundary value problems, J. math. anal. appl., 171, 301-320, (1992) · Zbl 0767.34047
[10] Aizicovici, S.; McKibben, M.; Reich, S., Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities, Nonlinear anal., 43, 233-251, (2001) · Zbl 0977.34061
[11] Chen, Y.; Nieto, J.J.; ORegan, D., Anti-periodic solutions for fully nonlinear first-order differential equations, Math. comput. modelling, 46, 1183-1190, (2007) · Zbl 1142.34313
[12] Wu, R., An anti-periodic Lasalle oscillation theorem, Appl. math. lett., (2007)
[13] Delvos, F.J.; Knoche, L., Lacunary interpolation by antiperiodic trigonometric polynomials, Bit, 39, 439-450, (1999) · Zbl 0931.42003
[14] Hale, J.K., Theory of functional differential equations, (1977), Springer-Verlag New York · Zbl 0425.34048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.