Global stability of discrete-time Cohen-Grossberg neural networks with impulses

Neurocomputing

Volumn 73, Issue 16-18, 2010, Pages 3132-3138

  Zhong, Shigang ^a   Li, Chuandong ^a   Liao, Xiaofeng ^a  

^a CHONGQING UNIVERSITY   (China)

Author keywords

Cohen Grossberg neural networks; Discrete time; Impulse; Time delay

Indexed keywords

COHEN-GROSSBERG NEURAL NETWORKS; DISCRETE-TIME; EQUILIBRIUM POINT; GLOBAL EXPONENTIAL STABILITY; GLOBAL STABILITY; HALANAY INEQUALITY; IMPULSE;

STABILITY CRITERIA; TIME DELAY; UNMANNED AERIAL VEHICLES (UAV);

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COHEN GROSSBERG NEURAL NETWORK; EQUILIBRIUM CONSTANT; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL; PROCESS MODEL; THEORY VALIDATION; VALIDATION PROCESS;

EID: 78650304530     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.06.014     Document Type: Article

References (40)

1. Cohen M.A., Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics 1983, SMC-13:815-821.
2. Liao X., Li C., Wong K.W. Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 2004, 17:1401-1414.
3. Li Y., Fan X. Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients. Applied Mathematical Modelling 2009, 33:2114-2120.
4. Arik S., Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Physics Letters A 2005, 341:410-421.
5. Arik S. An analysis of exponential stability of delayed neural networks with time varying delays. Neural Networks 2004, 17:1027-1031.
6. Liao X., Li C. Global attractivity of Cohen-Grossberg model with finite and infinite delays. Journal of Mathematical Analysis and Applications 2006, 315:244-262.
7. Liao X., Yang J., Guo S. Exponential stability of Cohen-Grossberg neural networks with delays. Communications in Nonlinear Science and Numerical Simulation 2008, 13:1767-1775.
8. Li C., Liao X. New algebraic conditions for global exponential stability of delayed recurrent neural networks. Neurocomputing 2005, 64:319-333.
9. Liao X., Liu Y., Guo S., Mai H. Asymptotic stability of delayed neural networks: A descriptor system approach. Communications in Nonlinear Science and Numerical Simulation 2009, 14:3120-3133.
10. Cao J., Feng G., Wang Y. Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions. Physica D: Nonlinear Phenomena 2008, 237:1734-1749.
11. Cao J., Li X. Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Physica D: Nonlinear Phenomena 2005, 212:54-65.
12. Cao J., Liang J. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. Journal of Mathematical Analysis and Applications 2004, 296:665-685.
13. Song Q., Cao J. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays. Journal of Computational and Applied Mathematics 2006, 197:188-203.
14. Song Q., Cao J. Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Journal of the Franklin Institute 2006, 343:705-719.
15. Li K., Song Q. Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms. Neurocomputing 2008, 72:231-240.
16. Li Y. Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays, Chaos. Solitons and Fractals 2004, 20:459-466.
17. Li Y., Yang L. Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays. Communication in Nonlinear Science and Numerical Simulation 2009, 14:3134-3140.
18. Li Y., Fan X. Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients. Applied Mathematical Modelling 2009, 33:2114-2120.
19. Li Y., Xing W., Lu L. Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons and Fractals 2006, 27:437-445.
20. Huang T., Li C., Chen G. Stability of Cohen-Grossberg neural networks with unbounded distributed delays. Chaos, Solitons & Fractals 2007, 34:992-996.
21. Song Q., Zhang J. Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Analysis: Real World Applications 2008, 9:500-510.
22. Song Q., Wang Z. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Physica A 2008, 387:3314-3326.
23. Li Y., Chen X., Zhao L. Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales. Neurocomputing 2009, 72:1621-1630.
24. Li C., Liao X. Impulsive stabilization of delayed neural networks with and without uncertainty. International Journal of Robust and Nonlinear Control 2007, 17:1489-1502.
25. Li C., Liao X. Complete and lag synchronization of hyperchaotic systems using small impulses. Chaos, Solitons & Fractals 2004, 22:857-867.
26. Li C., Liao X., Zhang R. Impulsive synchronization of nonlinear coupled chaotic systems. Physics Letters A 2004, 328:47-50.
27. Xia Y., Cao J., Cheng S. Global exponential stability of delayed cellular neural networks with impulses. Neurocomputing 2007, 70:2495-2501.
28. Li Y., Fan X, Zhao L. Positive periodic solutions of functional differential equations with impulses and a parameter. Computers & Mathematics with Applications 2008, 56:2556-2560.
29. Xiong W., Cao J. Global exponential stability of discrete-time Cohen-Grossberg neural networks. Neurocomputing 2005, 64:433-446.
30. Zhao H., Wang L. Stability and bifurcation for discrete-time Cohen-Grossberg neural network. Applied Mathematics and Computation 2006, 179:787-798.
31. Liu M. Global asymptotic stability analysis of discrete-time Cohen-Grossberg neural networks based on interval systems, nonlinear analysis: theory. Methods & Applications 2008, 69:2403-2411.
32. Kanellakopoulos I. A discrete-time adaptive nonlinear systems. IEEE Transactions on Automatic Control 1994, 39:2362-2365.
33. Liang J., Cao J., Ho D.W.C. Discrete-time bidirectional associative memory neural networks with variable delays. Physics Letters A 2005, 335:226-234.
34. Guo S., Huang L., Wang L. Exponential stability of discrete-time Hopfield neural networks. Computers & Mathematics with Applications 2004, 47:1249-1256.
35. Zhao H., Wang L., Ma C. Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay. Nonlinear Analysis: Real World Applications 2008, 9:103-113.
36. Liu X., Tang M., Martin R., Liu X. Discrete-time BAM neural networks with variable delays. Physics Letters A 2007, 367:322-330.
37. Zhou T., Liu Y., Liu Y. Existence and global exponential stability of periodic solution for discrete-time BAM neural networks. Applied Mathematics and Computation 2006, 182:1341-1354.
38. Zhou T., Liu Y., Li X., Liu Y. A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays. Chaos, Solitons & Fractals 2009, 39:332-341.
39. Liz E., Ferreiro J.B. A note on the global stability of generalized difference equations. Applied Mathematics Letters 2002, 15:655-659.
40. Halanay A. Differential Equations: Stability, Oscillations, Time Lags 1966, Academic Press, New York.