# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Periodic solutions of high-order Cohen-Grossberg neural networks with distributed delays. (English) Zbl 1221.37215
Summary: A class of high-order Cohen-Grossberg neural networks with distributed delays is investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of periodic solutions of such networks are established by using suitable Lypunov function and the properties of $M$-matrix. The results in this paper improve the earlier publications.
##### MSC:
 37N35 Dynamical systems in control 34K13 Periodic solutions of functional differential equations 34D23 Global stability of ODE 92B20 General theory of neural networks (mathematical biology)
##### References:
 [1] Townley, S.; Ilchmann, S.; Weiss, A.: Existence and learning of oscillations in recurrent neural networks, IEEE trans neural netw 11, 205-214 (2000) [2] Huang, Z.; Xia, Y.: Exponential periodic attractor of impulsive BAM networks with finite distributed delays, Chaos solitons fract 39, 373-384 (2009) · Zbl 1197.34124 · doi:10.1016/j.chaos.2007.04.014 [3] Guo, S.; Huang, L.: Periodic oscillotory for a class of neural networks with variable coefficients, Nonlinear anal: real world appl 6, 545-561 (2005) · Zbl 1080.34051 · doi:10.1016/j.nonrwa.2004.11.004 [4] Sun, J.; Wang, L.: Global exponential stability and periodic solutions of Cohen – Grossberg neural networks with continuously distributed delays, Physica D 208, 1-20 (2005) · Zbl 1086.34061 · doi:10.1016/j.physd.2005.05.009 [5] Zhou, T.; Chen, A.; Zhou, Y.: Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays, Phys lett A 343, 336-350 (2005) · Zbl 1194.34134 · doi:10.1016/j.physleta.2005.02.081 [6] Song, Q.; Cao, J.; Zhao, Z.: Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays, Nonlinear anal: real world appl 7, 65-80 (2006) · Zbl 1094.35128 · doi:10.1016/j.nonrwa.2005.01.004 [7] Ren, F.; Cao, J.: Periodic solutions for a class of higher-order Cohen – Grossberg type neural networks with delays, Comput math appl 54, 826-839 (2007) · Zbl 1143.34046 · doi:10.1016/j.camwa.2007.03.005 [8] Wang, H.; Liao, X.; Li, C.: Existence and exponential stability of periodic solution of BAM neural networks with impulse and time-varying delay, Chaos solitons fract 33, 1028-1039 (2007) · Zbl 1148.34049 · doi:10.1016/j.chaos.2006.01.112 [9] Song, Q.; Wang, Z.: An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays, Nonlinear anal: real world appl 8, 1224-1234 (2007) · Zbl 1125.34050 · doi:10.1016/j.nonrwa.2006.07.002 [10] Li, Y.; Wang, J.: Analysis on the global exponential stability and existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses, Comput math appl 56, 2256-2267 (2008) · Zbl 1165.34410 · doi:10.1016/j.camwa.2008.03.048 [11] Li, Y.; Chen, X.; Zhao, L.: Stability and existence of periodic solutions to delayed Cohen – Grossberg BAM neural networks with impulses on timescales, Neurocomputing 72, 1621-1630 (2009) [12] Yang, X.: Existence and global exponential stability of periodic solution for Cohen – Grossberg shunting inhibitory cellular neural networks with delays and impulses, Neurocomputing 72, 2219-2226 (2009) [13] Li, C.; Yang, S.: Existence and attractivity of of periodic solution for Cohen – Grossberg neural networks with time delays, Chaos solitons fract 35, 1235-1244 (2009) · Zbl 1198.34139 · doi:10.1016/j.chaos.2008.05.005 [14] Xiang, H.; Cao, J.: Exponential stability of periodic solution to Cohen – Grossberg-type BAM networks with time-varying delays, Neurocomputing 72, 1702-1711 (2009) [15] Ping, Z.; Lu, J.: Global exponential stability of impulsive Cohen – Grossberg neural networks with continuously distributed delays, Chaos solitons fract 41, 164-174 (2009) · Zbl 1198.34159 · doi:10.1016/j.chaos.2007.11.022 [16] Li, Z.; Li, K.: Stability analysis of impulsive Cohen – Grossberg neural networks with distributed delays and reaction – diffusion terms, Appl math model 33, 1337-1448 (2009) · Zbl 1168.35382 · doi:10.1016/j.apm.2008.01.016 [17] Varga, Richard S.: Matrix iterative analysis, (2000) [18] Fang, B.; Zhou, J.; Li, Y.: Matrix theory, (2004)