Existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays

Journal of Applied Mathematics and Computing

Volumn 28, Issue 1-2, 2008, Pages 461-472

  Zhang, Lijuan ^a,b   Shi, Bao ^a  

^a NAVAL AERONAUTICAL AND ASTRONAUTICAL UNIVERSITY   (China)

^b YANTAI UNIVERSITY   (China)

Author keywords

Almost periodic solution; Cellular neural networks; Exponential dichotomy; Fixed point theory; Global exponential stability

Indexed keywords

EID: 48749112419     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-008-0119-3     Document Type: Article

References (20)

1. 1. J. Cao A. Chen X. Huang 2005 Almost periodic attractor of delayed neural networks with variable coefficients Phys. Lett. A 340 104 120 05253305 10.1016/j.physleta.2005.04.021 Cao, J., Chen, A., Huang, X.: Almost periodic attractor of delayed neural networks with variable coefficients. Phys. Lett. A 340, 104–120 (2005)
2. 2. A. Chen L. Huang 2003 Existence and global exponential stability conditions of almost periodic solution in DCNNs with variable coefficients Southeast Asian Bull. Math. 26 1 11 10.1007/s100120200020 Chen, A., Huang, L.: Existence and global exponential stability conditions of almost periodic solution in DCNNs with variable coefficients. Southeast Asian Bull. Math. 26, 1–11 (2003)
3. 3. L.O. Chua L. Yang 1988 Cellular neural networks: Theory and application IEEE Trans. Circuits Syst. 35 1257 1272 0663.94022 10.1109/31.7600 960777 Chua, L.O., Yang, L.: Cellular neural networks: Theory and application. IEEE Trans. Circuits Syst. 35, 1257–1272 (1988)
4. 4. D. Danciu V. Räsvan 2005 Stability results for cellular neural networks with time delays Lect. Notes Comput. Sci. 3512 366 373 Danciu, D., Räsvan, V.: Stability results for cellular neural networks with time delays. Lect. Notes Comput. Sci. 3512, 366–373 (2005)
5. 5. A.M. Fink 1974 Almost Periodic Differential Equation Springer Berlin Fink, A.M.: Almost Periodic Differential Equation. Springer, Berlin (1974)
6. 6. I. Győri F. Hartung 2004 Stability results for cellular neural networks with delays Electron. J. Qual. Theory Differ. Equ. 13 1 14 Győri, I., Hartung, F.: Stability results for cellular neural networks with delays. Electron. J. Qual. Theory Differ. Equ. 13, 1–14 (2004)
7. 7. G.H. Hardy J.E. Littlewood G. Polya 1952 Inequalities 2 Cambridge University Press London 0047.05302 Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd edn. Cambridge University Press, London (1952)
8. 8. C.Y. He 1992 Almost Periodic Differential Equations Higher Education Publishing House Beijing He, C.Y.: Almost Periodic Differential Equations. Higher Education Publishing House, Beijing (1992)
9. 9. X. Huang J. Cao 2003 Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delays Phys. Lett. A 314 3 222 231 1052.82022 10.1016/S0375-9601(03)00918-6 1995884 Huang, X., Cao, J.: Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delays. Phys. Lett. A 314 (3), 222–231 (2003)
10. 10. H. Huang D.W.C. Ho J. Cao 2005 Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays Neural Netw. 18 161 170 10.1016/j.neunet.2004.11.002 Huang, H., Ho, D.W.C., Cao, J.: Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays. Neural Netw. 18, 161–170 (2005)
11. 11. J. Hu S.M. Zhong L. Liang 2006 Exponential stability analysis of stochastic delayed cellular neural network Chaos, Solitons Fractals 27 4 1006 1010 1084.68099 10.1016/j.chaos.2005.04.067 2166682 Hu, J., Zhong, S.M., Liang, L.: Exponential stability analysis of stochastic delayed cellular neural network. Chaos, Solitons Fractals 27 (4), 1006–1010 (2006)
12. 12. Y. Li 2004 Global stability and existence of periodic solutions of discrete delayed cellular neural networks Phys. Lett. A 333 51 61 1123.39302 10.1016/j.physleta.2004.10.022 2101961 Li, Y.: Global stability and existence of periodic solutions of discrete delayed cellular neural networks. Phys. Lett. A 333, 51–61 (2004)
13. 13. T. Roska C.W. Wu M. Balsi L.O. Chua 1992 Stability and dynamics of delay-type general and cellular neural networks IEEE Trans. Circuits Syst. 39 487 490 0775.92010 10.1109/81.153647 Roska, T., Wu, C.W., Balsi, M., Chua, L.O.: Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans. Circuits Syst. 39, 487–490 (1992)
14. 14. J. Wei S. Ruan 1999 Stability and bifurcation in a neural network model with two delays Physica D 130 255 272 1066.34511 1692866 Wei, J., Ruan, S.: Stability and bifurcation in a neural network model with two delays. Physica D 130, 255–272 (1999)
15. 15. Y. Zhang H.A. Pheng K.S. Leung 2001 Convergence analysis of cellular neural networks with unbounded delay IEEE Trans. Circuits Syst. 48 6 680 687 0994.82068 10.1109/81.928151 Zhang, Y., Pheng, H.A., Leung, K.S.: Convergence analysis of cellular neural networks with unbounded delay. IEEE Trans. Circuits Syst. 48 (6), 680–687 (2001)
16. 16. Y. Zhang H.A. Pheng P. Vadakkepat 2002 Absolute periodicity and absolute stability of neural networks with delays IEEE Trans. Circuits Syst. 49 2 256 261 10.1109/81.983875 Zhang, Y., Pheng, H.A., Vadakkepat, P.: Absolute periodicity and absolute stability of neural networks with delays. IEEE Trans. Circuits Syst. 49 (2), 256–261 (2002)
17. 17. Q. Zhang X.P. Wei J. Xu 2005 On global exponential stability of delayed cellular neural networks with time-varying delays Appl. Math. Comput. 162 679 686 1114.34337 10.1016/j.amc.2004.01.004 2111863 Zhang, Q., Wei, X.P., Xu, J.: On global exponential stability of delayed cellular neural networks with time-varying delays. Appl. Math. Comput. 162, 679–686 (2005)
18. 18. H. Zhao 2004 Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays Appl. Math. Comput. 154 683 695 1057.34099 10.1016/S0096-3003(03)00743-4 2072813 Zhao, H.: Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Appl. Math. Comput. 154, 683–695 (2004)
19. 19. W. Zheng J. Zhang 2005 Global exponential stability of a class of neural networks with variable delays Comput. Math. Appl. 49 5/6 895 902 1085.34061 10.1016/j.camwa.2004.03.015 2135221 Zheng, W., Zhang, J.: Global exponential stability of a class of neural networks with variable delays. Comput. Math. Appl. 49 (5/6), 895–902 (2005)
20. 20. W.L. Zhu J. Hu 2006 Stability analysis of stochastic delayed cellular neural networks by LMI approach Chaos, Solitons Fractals 29 1 171 174 1095.92003 10.1016/j.chaos.2005.08.049 2213344 Zhu, W.L., Hu, J.: Stability analysis of stochastic delayed cellular neural networks by LMI approach. Chaos, Solitons Fractals 29 (1), 171–174 (2006)