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Almost periodic solutions for impulsive neural networks with delay. (English) Zbl 1136.34332
The authors are interested in the existence and attractivety of almost periodic solutions for impulsive cellular neural networks with delay. They obtain a generalization of known results for the dynamics behavior of Hopfield neural networks with delay.

34K14Almost and pseudo-periodic solutions of functional differential equations
34K45Functional-differential equations with impulses
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
Full Text: DOI
[1] Mil’man, V. D.; Myshkis, A. D.: On the stability of motion in the presence of impulses. Siber. math. J. 1, 233-237 (1960)
[2] Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations: periodic solutions and applications. (1993) · Zbl 0815.34001
[3] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[4] Samoilenko, A. M.; Perestyuk, N. A.: Differential equations with impulse effect. (1987)
[5] Stamov, G. T.: Almost periodic solutions for forced perturbed impulsive differential equations. Appl. anal. 74, No. 1 -- 2, 45-56 (2000) · Zbl 1031.34005
[6] Stamov, G. T.: Separated and almost periodic solutions for impulsive differential equations. Note di mat. 20, No. 2, 105-113 (2000 -- 2001) · Zbl 1223.34013
[7] Stamov, G. T.: Existence of almost periodic solutions for strong stable impulsive differential equations. IMA J. Math. C. Inf 18, 153-160 (2001) · Zbl 0987.34040
[8] Azbelev, N. V.; Maksimov, V. P.; Rakhmatullina, L. F.: Introduction to the theory of functional differential equations. (1991) · Zbl 0725.34071
[9] Hale, J. K.: Theory of functional differential equations. (1977) · Zbl 0352.34001
[10] Hale, J. K.; Lunel, V.: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[11] Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-stage neurons. Proc. natl. Acad. sci. USA 81, 3088-3092 (1984)
[12] Anokhin, A. V.: On linear impulse system for functional differential equations. Sov. math. Dokl. 33, 220-223 (1986) · Zbl 0615.34064
[13] Gopalsamy, K.; Zhang, B. G.: On delay differential equations with impulses. J. math. Anal. appl. 139, 110-122 (1989) · Zbl 0687.34065
[14] Bainov, D. D.; Stamova, I. M.: Lypschitz stability of impulsive functional differential equations. Anziam j. 42, 504-515 (2001) · Zbl 0994.34064
[15] Bainov, D. D.; Stamova, I. M.: Strong stability of impulsive differential -- difference equations. Panam. math. J. 9, 87-95 (1999) · Zbl 0960.34064
[16] Luo, Z.; Shen, J.: Stability results for impulsive functional differential equations with infinite delays. J. comput. Appl. math. 131, 55-64 (2001) · Zbl 0988.34059
[17] Shen, J.: Existence and uniqueness of solutions for impulsive functional differential equations on the PC space with applications. Acta. sci. Natl. uni. Norm. hunan 24, 285-291 (1996)
[18] Shen, J.; Yan, J.: Razumikhin type stability theorems for impulsive functional differential equations. Nonlinear anal. 33, 519-531 (1998) · Zbl 0933.34083
[19] Stamova, I. M.; Stamov, G. T.: Lyapunov -- razumikhin method for impulsive functional differential equations and applications to the population dynamics. J. comput. Appl. math. 130, 163-171 (2001) · Zbl 1022.34070
[20] Cao, J.: Global exponential stability of Hopfield neural networks with delays. Int. J. Syst. sci. 32, No. 2, 233-236 (2001) · Zbl 1011.93091
[21] Cao, J.; Chen, A.; Huang, X.: Almost periodic attractor of delay neural networks with variable coefficients. Phys. lett. A 340, No. 1 -- 4, 104-120 (2005) · Zbl 1145.37308
[22] Chen, A.; Cao, J.: Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients. Appl. math. Comput. 134, No. 1, 125-140 (2003) · Zbl 1035.34080
[23] Huang, X.; Cao, J.: Almost periodic solutions of shunting inhibitory cellular neural networks with time-varying delays. Phys. lett. A 314, No. 3, 222-231 (2003) · Zbl 1052.82022