Stability Analysis of Impulsive Stochastic Fuzzy Cellular Neural Networks with Time-varying Delays and Reaction-diffusion Terms

Authors: Xinhua Zhang, Kelin Li

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059713

References:

[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)