Stability Analysis of Impulsive Stochastic Fuzzy Cellular Neural Networks with Time-varying Delays and Reaction-diffusion Terms
In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.
[1] T. Yang, L. Yang, C. Wu, L. Chua, "Fuzzy celluar neural networks:
Theory" in: Proceedings of IEEE International Workshop on Cellular
Neural Networks and Applications (1996) 181-186,
[2] T. Yang, L. Yang, "The global stability of fuzzy celluar neural networks",
IEEE Trans. Cric. Syst. I 43(1996) 880-883.
[3] Y. Liu, W. Tang, "Exponential stability of fuzzy cellular neural networks
with constant and time-varying delays", Phys. Lett. A 323(2004) 224-233.
[4] K. Yuan, J. Cao, J. Deng, "Exponential stability and periodic solutions
of fuzzy cellular neural networks with time-varying delays", Neurocomputing
69(2006)1619-1627.
[5] T. Huang, "Exponential stability of fuzzy cellular neural networks with
distributed delay", Phys. Lett. A 351 (2006) 48-52.
[6] T. Huang, "Exponential stability of delayed fuzzy cellular neural networks
with diffusion", Chaos Solitons & Fractals 31(2007)658-664.
[7] Q. Zhang, R. Xiang, "Global asymptotic stability of fuzzy cellular neural
networks with time-varying delays", Phys. Lett. A 372 (2008) 3971-3977.
[8] Q. Song, J. Cao, "Dynamical behaviors of discrete-time fuzzy cellular
neural networks with variable delays and impulses", Journal of the
Franklin Institute 345(2007) 39-59.
[9] H. Zhao, N. Ding, Ling Chen, "Almost sure exponential stability of
stochastic fuzzy cellular neural networks with delays", Chaos, Solitons
& Fractals 40 (2009) 1653-1659.
[10] S. Wang, D. Fu, M. Xu, D. Hu, "Advanced fuzzy cellular neural network:
Application to CT liver images", Artificial Intelligence in Medicine 39
(2007) 65-77.
[11] Wang S., Korris F.L. Chung, Fu D., "Applying the improved fuzzy cellular
neural network IFCNN to white blood cell detection", Neurocomputing
70 (2007) 1348-1359.
[12] K. Li, "Global exponential stability of impulsive fuzzy cellular neural
networks with delays and diffusion", Int. J. Bifurc. Chaos 19 (2009) 245-
261.
[13] K. Li, Q. Song, "Exponential stability of impulsive Cohen-Grossberg
neural networks with time-varying delays and reaction-diffusion terms",
Neurocomputing 72 (2008) 231-240.
[14] Z. Li, K. Li, "Stability analysis of impulsive Cohen-Grossberg neural
networks with distributed delays and reaction-diffusion terms", Appl.
Math. Model. 33 (2009) 1337-1348.
[15] J. Qiu, "Exponential stability of impulsive neural networks with timevarying
delays and reaction-diffusion terms", Neurocomputing 70 (2007)
1102-1108.
[16] J. G. Lu, "Global exponential stability and periodicity of reactiondiffusion
delayed recurrent neural networks with Dirichlet boundary
conditions", Chaos, Solitons & Fractals 35 (2008) 116-125.
[17] J. G. Lu, L. J. Lu, "Global exponential stability and periodicity of
reaction-diffusion recurrent neural networks with distributed delays and
Dirichlet boundary conditions", Chaos, Solitons & Fractals 39 (2009)
1538-1549.
[18] Q. Song, J. Cao, "Dynamics of bidirectional associative memory networks
with distributed delays and reaction-diffusion terms", Nonlinear
Analysis: Real World Applications 8 (2007) 345-361.
[19] Q. Song, J. Cao, "Global exponential robust stability of Cohen-
Grossberg neural network with time-varying delays and reaction-diffusion
terms", Journal of the Franklin Institute 343 (2006) 705-719.
[20] H. Zhao, K. Wang, "Dynamical behaviors of Cohen-Grossberg neural
networks with delays and reaction-diffusion terms", Neurocomputing 70
(2006) 536-543.
[21] X. Wang, D. Xu, "Global exponential stability of impulsive fuzzy
cellular neural networks with mixed delays and reaction-diffusion terms",
Chaos, Solitons & Fractals 42 (2009) 2713-2721.
[22] L. Wang, Y. Gao, "Global exponential robust stability of reactiondiffusion
interval neural networks with time-varying delays", Physics
Letters A 350 (2006) 342-348.
[23] L. Wang, R. Zhang, Y. Wang, "Global exponential stability of reactiondiffusion
cellular neural networks with S-type distributed time delays",
Nonlinear Analysis: Real World Applications 10 (2009) 1101C1113.
[24] P. Liu, F. Yi, Q. Guo, J. Yang, W. Wu, "Analysis on global exponential
robust stability of reaction-diffusion neural networks with S-type distributed
delays", Physica D: Nonlinear Phenomena 237 (2008) 475-485.
[25] K. Li, "Stability analysis for impulsive Cohen-Grossberg neural networks
with time-varying delays and distributed delays", Nonlinear Analysis:
Real World Applications 10 (2009) 2784-2798.
[26] Y. Yang, J. Cao, "Stability and periodicity in delayed cellular neural
networks with impulsive effects", Nonlinear Analysis: Real World Applications
8 (2007) 362-374.
[27] D. Xu, Z. Yang, "Impulsive delay differential inequality and stability of
neural networks", J. Math. Anal. Appl. 305 (2005) 107-120.
[28] Z. Yang, D. Xu, "Impulsive effects on stability of Cohen-Grossberg
neural networks with variable delays", Appl. Math. Comput. 177 (2006)
63-78.
[29] Q. Song, Z. Wang, "Stability anylysis of impulsive stochastic Cohen-
Grossberg neural networks with mined time delays", Physica A 287
(2008) 3314-3326.
[30] X. Li, "Existence and global exponential stability of periodic solution
for delayed neural networks with impulsive and stochastic effects",
Neurocomputing 73 (2010) 749-758.
[31] L. Xu, D. Xu, "Exponential p-stability of impulsive stochastic neural
networks with mixed delays", Chaos, Solitons & Fractals 41 (2009) 263-
272.
[32] X. Wang, Q. Guo, D. Xu, "Exponential p-stability of impulsive stochastic
Cohen-Grossberg neural networks with mixed delays", Mathematics
and Computers in Simulation 79 (2009)1698-1710.
[33] Xiaolin Li . Jinde Cao, "Delay-independent exponential stability of
stochastic Cohen-Grossberg neural networks with time-varying delays and
reaction-diffusion terms", Nonlinear dyn. 50 (2007) 363-371.
[34] Q. Luo, F. Deng, X. Mao, J. Bao, Y. Zhang, "Theory and application
of stability for stochastic reaction diffusion systems", Science in China,
Series F: Information Sciences 51 (2008) 158-170.
[35] Q. Luo, Y. Zhang, "Almost sure exponential stability of stochastic
reaction diffusion systems", Nonlinear Analysis, Theory, Methods and
Applications 71 (2009) e487-e493 .
[36] S. Haykin, "Neural Networks", Prentice-Hall, Englewood Cliffs, NJ
(1994)
[1] T. Yang, L. Yang, C. Wu, L. Chua, "Fuzzy celluar neural networks:
Theory" in: Proceedings of IEEE International Workshop on Cellular
Neural Networks and Applications (1996) 181-186,
[2] T. Yang, L. Yang, "The global stability of fuzzy celluar neural networks",
IEEE Trans. Cric. Syst. I 43(1996) 880-883.
[3] Y. Liu, W. Tang, "Exponential stability of fuzzy cellular neural networks
with constant and time-varying delays", Phys. Lett. A 323(2004) 224-233.
[4] K. Yuan, J. Cao, J. Deng, "Exponential stability and periodic solutions
of fuzzy cellular neural networks with time-varying delays", Neurocomputing
69(2006)1619-1627.
[5] T. Huang, "Exponential stability of fuzzy cellular neural networks with
distributed delay", Phys. Lett. A 351 (2006) 48-52.
[6] T. Huang, "Exponential stability of delayed fuzzy cellular neural networks
with diffusion", Chaos Solitons & Fractals 31(2007)658-664.
[7] Q. Zhang, R. Xiang, "Global asymptotic stability of fuzzy cellular neural
networks with time-varying delays", Phys. Lett. A 372 (2008) 3971-3977.
[8] Q. Song, J. Cao, "Dynamical behaviors of discrete-time fuzzy cellular
neural networks with variable delays and impulses", Journal of the
Franklin Institute 345(2007) 39-59.
[9] H. Zhao, N. Ding, Ling Chen, "Almost sure exponential stability of
stochastic fuzzy cellular neural networks with delays", Chaos, Solitons
& Fractals 40 (2009) 1653-1659.
[10] S. Wang, D. Fu, M. Xu, D. Hu, "Advanced fuzzy cellular neural network:
Application to CT liver images", Artificial Intelligence in Medicine 39
(2007) 65-77.
[11] Wang S., Korris F.L. Chung, Fu D., "Applying the improved fuzzy cellular
neural network IFCNN to white blood cell detection", Neurocomputing
70 (2007) 1348-1359.
[12] K. Li, "Global exponential stability of impulsive fuzzy cellular neural
networks with delays and diffusion", Int. J. Bifurc. Chaos 19 (2009) 245-
261.
[13] K. Li, Q. Song, "Exponential stability of impulsive Cohen-Grossberg
neural networks with time-varying delays and reaction-diffusion terms",
Neurocomputing 72 (2008) 231-240.
[14] Z. Li, K. Li, "Stability analysis of impulsive Cohen-Grossberg neural
networks with distributed delays and reaction-diffusion terms", Appl.
Math. Model. 33 (2009) 1337-1348.
[15] J. Qiu, "Exponential stability of impulsive neural networks with timevarying
delays and reaction-diffusion terms", Neurocomputing 70 (2007)
1102-1108.
[16] J. G. Lu, "Global exponential stability and periodicity of reactiondiffusion
delayed recurrent neural networks with Dirichlet boundary
conditions", Chaos, Solitons & Fractals 35 (2008) 116-125.
[17] J. G. Lu, L. J. Lu, "Global exponential stability and periodicity of
reaction-diffusion recurrent neural networks with distributed delays and
Dirichlet boundary conditions", Chaos, Solitons & Fractals 39 (2009)
1538-1549.
[18] Q. Song, J. Cao, "Dynamics of bidirectional associative memory networks
with distributed delays and reaction-diffusion terms", Nonlinear
Analysis: Real World Applications 8 (2007) 345-361.
[19] Q. Song, J. Cao, "Global exponential robust stability of Cohen-
Grossberg neural network with time-varying delays and reaction-diffusion
terms", Journal of the Franklin Institute 343 (2006) 705-719.
[20] H. Zhao, K. Wang, "Dynamical behaviors of Cohen-Grossberg neural
networks with delays and reaction-diffusion terms", Neurocomputing 70
(2006) 536-543.
[21] X. Wang, D. Xu, "Global exponential stability of impulsive fuzzy
cellular neural networks with mixed delays and reaction-diffusion terms",
Chaos, Solitons & Fractals 42 (2009) 2713-2721.
[22] L. Wang, Y. Gao, "Global exponential robust stability of reactiondiffusion
interval neural networks with time-varying delays", Physics
Letters A 350 (2006) 342-348.
[23] L. Wang, R. Zhang, Y. Wang, "Global exponential stability of reactiondiffusion
cellular neural networks with S-type distributed time delays",
Nonlinear Analysis: Real World Applications 10 (2009) 1101C1113.
[24] P. Liu, F. Yi, Q. Guo, J. Yang, W. Wu, "Analysis on global exponential
robust stability of reaction-diffusion neural networks with S-type distributed
delays", Physica D: Nonlinear Phenomena 237 (2008) 475-485.
[25] K. Li, "Stability analysis for impulsive Cohen-Grossberg neural networks
with time-varying delays and distributed delays", Nonlinear Analysis:
Real World Applications 10 (2009) 2784-2798.
[26] Y. Yang, J. Cao, "Stability and periodicity in delayed cellular neural
networks with impulsive effects", Nonlinear Analysis: Real World Applications
8 (2007) 362-374.
[27] D. Xu, Z. Yang, "Impulsive delay differential inequality and stability of
neural networks", J. Math. Anal. Appl. 305 (2005) 107-120.
[28] Z. Yang, D. Xu, "Impulsive effects on stability of Cohen-Grossberg
neural networks with variable delays", Appl. Math. Comput. 177 (2006)
63-78.
[29] Q. Song, Z. Wang, "Stability anylysis of impulsive stochastic Cohen-
Grossberg neural networks with mined time delays", Physica A 287
(2008) 3314-3326.
[30] X. Li, "Existence and global exponential stability of periodic solution
for delayed neural networks with impulsive and stochastic effects",
Neurocomputing 73 (2010) 749-758.
[31] L. Xu, D. Xu, "Exponential p-stability of impulsive stochastic neural
networks with mixed delays", Chaos, Solitons & Fractals 41 (2009) 263-
272.
[32] X. Wang, Q. Guo, D. Xu, "Exponential p-stability of impulsive stochastic
Cohen-Grossberg neural networks with mixed delays", Mathematics
and Computers in Simulation 79 (2009)1698-1710.
[33] Xiaolin Li . Jinde Cao, "Delay-independent exponential stability of
stochastic Cohen-Grossberg neural networks with time-varying delays and
reaction-diffusion terms", Nonlinear dyn. 50 (2007) 363-371.
[34] Q. Luo, F. Deng, X. Mao, J. Bao, Y. Zhang, "Theory and application
of stability for stochastic reaction diffusion systems", Science in China,
Series F: Information Sciences 51 (2008) 158-170.
[35] Q. Luo, Y. Zhang, "Almost sure exponential stability of stochastic
reaction diffusion systems", Nonlinear Analysis, Theory, Methods and
Applications 71 (2009) e487-e493 .
[36] S. Haykin, "Neural Networks", Prentice-Hall, Englewood Cliffs, NJ
(1994)
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53825", author = "Xinhua Zhang and Kelin Li", title = "Stability Analysis of Impulsive Stochastic Fuzzy Cellular Neural Networks with Time-varying Delays and Reaction-diffusion Terms", abstract = "In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.
", keywords = "Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.", volume = "4", number = "1", pages = "21-8", }
