154
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Almost periodic solutions of impulsive integro‐differential neural networksFootnote*

&
Pages 505-516 | Received 14 Feb 2010, Published online: 10 Feb 2011

References

  • Agarwal , R. , Diagana , T. and Hernandez , E. 2007 . Weighted pseudo almost periodic solutions to some partial neutral functional differential equations . J. Nonlinear Convex Anal. , 8 (3) : 397 – 415 .
  • Ahmad , S. and Stamov , G. T. 2009 . Almost periodic solutions of n‐dimensional impulsive competitive systems . Nonlinear Anal.: Real World Appl. , 10 (3) : 1846 – 1853 . doi:10.1016/j.nonrwa.2008.02.020.
  • Ahmad , S. and Stamov , G.T. 2009 . On almost periodic periodic processes in impulsive competitive systems with delay and impulsive perturbations . Nonlinear Anal.: Real World Appl. , 10 (5) : 2857 – 2863 . doi:10.1016/j.nonrwa.2008.09.003.
  • Akhmet , M.U. , Alzabut , J.O. and Zafer , A. 2006 . Perron's theorem for linear impulsive differential equations with distributed delay . J. Comput. Appl. Math. , 193 (1) : 204 – 218 . doi:10.1016/j.cam.2005.06.004.
  • Akhmet , M.U. , Alzabut , J.O. and Zafer , A. 2008 . On periodic solutions of linear impulsive differential systems . Dyn. Contin. Discrete Impuls. Syst. , A 15 (5) : 621 – 631 .
  • Akhmet , M.U. and Turan , M. 2006 . The differential equations on time scales through impulsive differential equations . Nonlinear Anal. , 65 : 2043 – 2060 . doi:10.1016/j.na.2005.12.042.
  • Arik , S. and Tavanoglu , V. 2000 . On the global asymptotic stability of delayed cellular neural networks . IEEE Trans. Circuits Systems‐I , 47 : 571 – 574 . doi:10.1109/81.841859.
  • Bai , C. 2008 . Stability analysis of Cohen‐Grossberg BAM neural networks with delays and impulses . Chaos Solitons Fractals , 35 : 263 – 267 . doi:10.1016/j.chaos.2006.05.043.
  • Bainov , D.D. and Covachev , V. 1994 . Impulsive Differential Equations with a Small Parameters , World Scientific .
  • Bainov , D.D. and Pavel , S. 1993 . “ Pitman Monographs and Surveys in Pure and Applied Mathematics ” . In Impulsive Differential Equations: Periodic Solutions and Applications. Vol. 66 , New York
  • Cao , J. 1999 . Periodic solutions and exponential stability in delayed cellular neural networks . Phys. Rev. E , 60 : 3244 – 3248 . doi:10.1103/PhysRevE.60.3244.
  • Cao , J. 2001 . Global exponential stability of Hopfield neural networks . Int. J. Systems Sci. , 32 : 233 – 236 . doi:10.1080/00207720117783.
  • Cao , J. and Wang , L. 2002 . Exponential stability and periodic oscillatory solution in BAM networks with delays . IEEE Trans. Neural Networks , 13 (2) : 457 – 463 . doi:10.1109/72.991431. PMid:18244446
  • Chen , A. and Cao , J. 2003 . Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients . Appl. Math. Comput. , 134 : 125 – 140 . doi:10.1016/S0096–3003 (01)00274–0.
  • Cuevas , C. , Hernandez , E. and Rabelo , M. 2009 . The existence of solutions for impulsive neutral functional differential equations . Computers Math. Appl. , 58 (4) : 744 – 757 . doi:10.1016/j.camwa.2009.04.008.
  • Ait Dads , E. and Arino , O. 1996 . Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations . Nonlinear Anal. , 27 (4) : 361 – 386 .
  • Diblik , J. and Koksch , N. 2006 . Existence of global solutions of delayed differential equations via retract approach . Nonlinear Anal. , 64 : 1153 – 1170 . doi:10.1016/j.na.2005.06.030.
  • Gao , M. and Cui , B. 2009 . Global robust exponential stability of discrete‐time interval BAM neural networks with time‐varying delays . Appl. Math. Modeling , 33 (3) : 1270 – 1284 . doi:10.1016/j.apm.2008.01.019.
  • Gu , H. , Jiang , H. and Teng , Z. 2009 . BAM‐type impulsive neural networks with time‐varying delays . Nonlinear Anal.: Real World Appl. , 10 (5) : 3059 – 3072 . doi:10.1016/j.nonrwa.2008.10.039.
  • Huo , H. and Li , W. 2009 . Dynamics of continuous‐time bidirectional associative memory neural networks with impulses and their discrete counterparts . Chaos Solitons Fractals , 42 (4) : 2218 – 2229 . doi:10.1016/j.chaos.2009.03.118.
  • Lakshmikanthan , V. , Bainov , D. and Simeonov , P. 1989 . Theory of Impulsive Differential Equations , NJ : World Scientific .
  • Li , Y. 2004 . Existence and stability of periodic solutions for Cohen‐Grossberg neural networks with multiple delays . Chaos Solitons Fractals , 20 : 459 – 466 . doi:10.1016/S0960–0779 (03)00406–5.
  • Luo , Z. and Shen , J. 2001 . Stability results for impulsive functional differential equations with infinite delays . J. Comput. Appl. Math. , 131 ((1/2)) : 55 – 64 . doi:10.1016/S0377–0427 (00)00323‐X.
  • Mohamad , S. and Gopalsamy , K. 2003 . Exponential stability of continuous time and discrete time cellular neural networks . Appl. Math. Comput. , 135 : 17 – 38 . doi:10.1016/S0096–3003 (01)00299–5.
  • Ping , Z.W. and Lu , J.G. 2009 . Global exponential stability of impulsive Cohen‐Grossberg neural networks with continuously distributed delays . Chaos Solitons Fractals , 41 (1) : 164 – 174 . doi:10.1016/j.chaos.2007.11.022.
  • Rao , M. Rama Mohana , Sathanatham , M. and Sivasundaram , S. 1990 . Asymptotuc behavior of solutions of Vollterra systems with impulsive effect . Appl. Math. Comput. , 31 : 195 – 211 .
  • Samoilenko , A.M. and Perestyuk , N.A. 1995 . Impulsive Differential Equations. , Singapore : World Scientific . doi:10.1142/9789812798664.
  • Stamov , G. T. 2007 . Almost periodic solutions of impulsive differential equations with time‐varying delay on the PC space . Nonlinear Stud. , 14 (3) : 269 – 279 .
  • Stamov , G.T. 2004 . Impulsive cellular neural networks and almost periodicity . Proc. Japan Acad. Ser. A Math. Sci. , 80 (10) : 198 – 203 . doi:10.3792/pjaa.80.198.
  • Stamov , G.T. and Petrov , N. 2008 . Lyapunov‐Razumikhin method for existence of almost periodic solutions of impulsive differential‐difference equations . Nonlinear Stud. , 15 (2) : 151 – 163 .
  • Stamov , G.T. and Stamova , I.M. 2007 . Almost periodic solutions for impulsive neutral networks with delay . Appl. Math. Modeling , 31 : 1263 – 1270 . doi:10.1016/j.apm.2006.04.008.
  • Sun , J. , Wang , Q. and Gao , H. 2009 . Periodic solution for nonautonomous cellular neural networks with impulses . Chaos Solitons Fractals , 40 (3) : 1423 – 1427 . doi:10.1016/j.chaos.2007.09.027.
  • Wen , Z. and Sun , J. 2009 . Stability analysis of delayed CohenU‐Grossberg BAM neural networks with impulses via nonsmooth analysis . Chaos Solitons Fractals , 42 (3) : 1829 – 1837 . doi:10.1016/j.chaos.2009.03.090.
  • Wu , H. and Shan , C. 2009 . Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses . Appl. Math. Modeling , 33 (6) : 2564 – 2574 . doi:10.1016/j.apm.2008.07.022.
  • Wu , W. , Cui , B.T. and Huang , M. 2007 . Global asymptotic stability of delayed Cohen‐Grossberg neural networks . Chaos Solitons Fractals , 34 : 872 – 877 . doi:10.1016/j.chaos.2006.03.111.
  • Xia , Y. , Cao , J. and Huang , Z. 2007 . Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses . Chaos Solitons Fractals , 34 : 1599 – 1607 . doi:10.1016/j.chaos.2006.05.003.
  • Yang , X. , Cui , X. and Long , Y. 2009 . Existence and global exponential stability of periodic solution of a cellular neural networks difference equation with delays and impulses . Neural Networks , 22 (7) : 970 – 976 . doi:10.1016/j.neunet.2009.04.006. PMid:19442487
  • Yucel , E. and Arik , S. 2009 . Novel results for global robust stability of delayed neural networks . Chaos Solitons Fractals , 39 (4) : 1604 – 1614 . doi:10.1016/j.chaos.2007.06.052.
  • Zaidman , S. 1985 . Almost periodic functions in abstrac spaces , Boston, MA : Research Notes in Mathematics .
  • Zhang , C. 2003 . Almost Periodic Type and Ergodicity , Kluwer Academic Publishers and Science Press .
  • Zhang , L. and Si , L.G. 2008 . Existence and exponential stability of almost periodic solution for BAM neural networks with variable coefficients and delays . Appl. Math. Comput. , 194 : 215 – 223 . doi:10.1016/j.amc.2007.04.044.
  • Zhou , J. and Li , S. 2009 . Global exponential stability of impulsive BAM neural networks with distributed delays . Neurocomputing , 72 ((7–9)) : 1688 – 1693 . doi:10.1016/j.neucom.2008.08.008.
  • The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.