# Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Qianhong Zhang; Lihui Yang; Daixi Liao

International Journal of Applied Mathematics and Computer Science (2011)

- Volume: 21, Issue: 4, page 649-658
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topQianhong Zhang, Lihui Yang, and Daixi Liao. "Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays." International Journal of Applied Mathematics and Computer Science 21.4 (2011): 649-658. <http://eudml.org/doc/208077>.

@article{QianhongZhang2011,

abstract = {Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.},

author = {Qianhong Zhang, Lihui Yang, Daixi Liao},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {fuzzy cellular neural networks; global exponential stability; periodic solution; coincidence degree},

language = {eng},

number = {4},

pages = {649-658},

title = {Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays},

url = {http://eudml.org/doc/208077},

volume = {21},

year = {2011},

}

TY - JOUR

AU - Qianhong Zhang

AU - Lihui Yang

AU - Daixi Liao

TI - Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

JO - International Journal of Applied Mathematics and Computer Science

PY - 2011

VL - 21

IS - 4

SP - 649

EP - 658

AB - Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

LA - eng

KW - fuzzy cellular neural networks; global exponential stability; periodic solution; coincidence degree

UR - http://eudml.org/doc/208077

ER -

## References

top- Arik, S. and Tavsanoglu, V. (2005). Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing 68: 161-176.
- Cao, J. (2003). Global asympotic stability of delayed bidirectional associative memory neural networks, Applied Mathematics and Computation 142(2): 333-339. Zbl1031.34074
- Cao, J. and Dong, M. (2003). Exponential stability of delayed bidirectional associative memory neural networks, Applied Mathematics and Computation 135(1): 105-112. Zbl1030.34073
- Cao, J. and Wang, L. (2002). Exponential stability and periodic oscilatory solution in BAM networks with delays, IEEE Transactions on Neural Networks 13(2): 457-463.
- Chen, A., Cao, J. and Huang, L. (2004). Exponential stability of BAM neural networks with transmission delays, Neurocomputing 57: 435-454.
- Gaines, R.E. and Mawhin, J.L. (1990). Coincidence Degree and Nolinear Differential Equations, Springer-Verlag, Berlin/New York, NY.
- Gopalsmy, K. and He, X.Z. (1994). Delay-independent stability in bi-directional associative memory networks, IEEE Transactions on Neural Networks 5(6): 998-1002.
- Huang, T. (2006). Exponential stability of fuzzy cellular neural networks with distributed delay, Physics Letters A 351(1): 48-52. Zbl1234.82016
- Kosto, B. (1987). Adaptive bi-directional associative memories, Applied Optics 26(23): 4947-4960.
- Kosto, B. (1988). Bi-directional associative memories, IEEE Transactions on Systems, Man, and Cybernetics 18(1): 49-60.
- Liao, X.F. and Yu, J.B. (1998). Qualitative analysis of bi-directional associative memory with time delay, International Journal of Circuit Theory and Applications 26(3): 219-229. Zbl0915.94012
- Liu, B.W. and Huang, L.H. (2006). Existence and exponential stability of periodic solutions for cellular neural networks with time-varying delays, Physics Letters A 349(6): 474-483. Zbl1195.34061
- Liu, Y.Q. and Tang, W.S. (2004). Exponential stability of fuzzy cellular neural networks with costant and time-varying delays, Physics Letters A 323(3): 224-233. Zbl1118.81400
- Liu, Y.Q. and Tang, W.S. (2006). Existence and exponential stability of periodic solution for bam neural networks with periodic coefficients and delays, Neurocomputing 69(16): 2152-2160.
- Liu, Z., Chen, A. and Huang, L. (2003). Existence and global exponential stability of periodic solution to self-connection BAM neural networks with delays, Physics Letters A 328(2): 127-143. Zbl1134.34329
- Liu, Z., Zhang, H. and Wang, Z. (2009). Novel stability criterions of a new fuzzy cellular neural networks with timevarying delays, Neurocomputing 72(4): 1056-1064.
- Niu, S., Jiang, H. and Teng, Z. (2008). Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays, Neurocomputing 71(13): 2929-2936.
- Raja, R., Sakthivel, R., Anthoni, S.M. and Kim, H. (2011). Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays, International Journal of Applied Mathematics and Computer Science 21(1): 127-135, DOI: 10.2478/v10006-011-0009-y. Zbl1221.93265
- Tian, A., Gai, M., Shi, B. and Zhang, Q. (2010). Existence and exponential stability of periodic solution for a class of Cohen-Grossberg-type BAM neural networks, Neurocomputing 73(16): 3147-3159.
- Wang, Z., Zhang, H. and Yu, W. (2007). Robust exponential stability analysis of neural networks with multiple time delays, Neurocomputing 70(13): 2534-2543.
- Yang, T. and Yang, L.B. (1996). The global stability of fuzzy cellular neural networks, IEEE Transactions on Circuits and Systems 1: Fundamental Theory and Applications 43(10): 880-883.
- Yang, T., Yang, L.B., Wu, C.W. and Chua, L.O. (1996). Fuzzy cellular neural networks: Theory, 4th IEEE International Workshop on Cellular Neural Networks and Their Applications, Seville, Spain, pp. 181-186.
- Yuan, K., Cao, J. and Deng, J. (2006). Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays, Neurocomputing 69(13): 1619-1627.
- Zhang, Q. and Luo, W. (2009). Global exponential stability of fuzzy BAM neural networks with time-varying delays, Chaos, Solitons and Fractals 42(4): 2239-2245. Zbl1198.34172
- Zhang, Q. and Xiang, R. (2008). Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Physics Letters A 372(22): 3971-3978. Zbl1220.34098
- Zhao, H. (2002). Global exponential stability of bidirectional associative memory neural networks with distributed delays, Physics Letters A 297(3): 182-190. Zbl0995.92002
- Zhao, H. (2006). Exponential stability and periodic oscillatory of bidirectional associative memory neural networks involving delays, Neurocomputing 69(4): 424-448.

## Citations in EuDML Documents

top- Yang Liu, Rongjiang Yang, Jianquan Lu, Bo Wu, Xiushan Cai, Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality
- Qiaoling Chen, Zhidong Teng, Zengyun Hu, Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.