Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks
In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.
[1] B. Kosto, Adaptive bi-directional associative memories, Appl. Opt. 26
(1987) 4947-4960.
[2] B. Kosto, Bi-directional associative memories, IEEE Trans.Syst. Man
Cybernet.18(1988)49-60.
[3] B. Kosto, Neural Networks and Fuzzy Systems:A Dynamical Systems
Approach to Machine Intelligence, Prentice-Hall, Englewood Cliffs,
NJ, 1992,38.
[4] K. Gopalsmy and X. Z. He, Delay-independent stability in bi-directional
associative memory networks, IEEE Trans. Neural Networks 5 (1994)
998-1002.
[5] J. Cao and L. Wang, Periodic oscillatory solution of bidirectional
associative memory networks with delays, Phys. Rev. E 61 (2000)
1825-1828.
[6] B. Liu and L. Huang, Global exponential stability of BAM neural
networks with recent-history distributed delays and impulse, Neurocomputing
69 (2006) 2090-2096.
[7] J. Cao and L. Wang, Exponential stability and periodic oscilatory
solution in BAM networks with delays, IEEE Trans. Neural Networks
13 (2002) 457-463.
[8] H. Zhao, Global exponential stability of bidirectional associative memory
neural networks with distributed delays, Phys. Lett. A 297 (2002) 182-
190.
[9] J. Zhang and Y. Yang, Global stability analysis of bidirectional
associative memory neural networks with time delay, Int.J.Ciruit
Theor.Appl.29(2001)185-196.
[10] X. F. Liao, K.W. Wong and S. Z. Yang, Convergence dynamics of hybrid
bidirectional associative memory neural networks with distributed delays,
Phys. Lett. A 316 (2003) 55-64.
[11] X. F. Liao and J. B. Yu, Qualitative analysis of bi-directional associative
memory with time delay, Int. J. Circ. Theory Appl. 26(1998)219-229.
[12] J. Cao and Q. Jiang, An analysis of periodic solutions of bi-directional
associative memory networks with time-varying delays, Phys. Lett. A
330 (2004) 203-213.
[13] A. Chen, J. Cao and L. Huang, Exponential stability of BAM neural
networks with transmission delays, Neurocomputing 57 (2004) 435-454.
[14] A. Chen, L. Huang, J. Cao, Existence and stability of almost periodic
solution for BAM neural networks with delays, Appl. Math. Comput.
137 (2003) 177-193.
[15] A. Chen, L. Huang, Z. Liu and J. Cao, Periodic bidirectional
associative memory neural networks with distributed delays, Journal
of Math. Analys. and Appl. 317 (2006) 80-102.
[16] Z. Liu, A. Chen, J. Cao and L. Huang, Existence and global
exponential stability of almost periodic solutions of BAM neural networks
with continuously distributed delays, Phys. Lett. A 319 (2003) 305-316.
[17] S. J. Guo, L. H. Huang, B. X. Dai and Z. Z. Zhang, Global existence
of periodic solutions of BAM neural networks with variable coefficients,
Phys. Lett. A 317(2003) 97-106.
[18] J. Cao, A set of stability criteria for delayed cellular neural networks,
IEEE Trans. Circuits Systems I 48 (4) (2001) 494-498.
[19] J. Cao, Global stability conditions for delayed CNNs, IEEE Trans.
Circuits Systems I 48(2001) 1330-1333.
[20] J. Cao and J. Wang, Global asymptotic stability of general class
of recurrent neural networks with time-varying delays, IEEE Trans.
Circuits Systems I 50 (2003)34-44.
[21] J. Cao, New results concerning exponential stability and periodic
solutions of delayed cellular neural networks, Phys. Lett. A 307 (2003)
136-147.
[22] J. Cao and J. Wang, Absolute exponential stability of recurrent neural
networks with Lipschitz-continuous activation functions and time delays,
Neural Networks 17 (2004) 379-390.
[23] J. Cao and J. Wang, Global exponential stability and periodicity of
recurrent neural networks with time delays, IEEE Trans. Circuits
Systems I 52 (2005)920-931.
[24] J. Cao and D. W. C. Ho, A general framework for global asymptotic
stability analysis of delayed neural networks based on LMI approach,
Chaos Solitons Fractals 24 (2005) 1317-1329.
[25] J. Cao, D. Huang and Y. Qu, Global robust stability of delayed
recurrent neural networks , Chaos Solitons Fractals 23 (2005)221-=229.
[26] Q. Song, Z. Zhao and Y. Li, Global exponential stability of BAM neural
networks with distributed delays and reactionCdiffusion terms, Phys Lett.
A 335(2005)213-225.
[27] T. Yang and L. B. Yang, The global stability of fuzzy cellular neural
networks, IEEE Trans. Circ. Syst. I 43(1996)880-883.
[28] T. Yang,L. B.Yang.,C. W.Wu and L. O.Chua, Fuzzy cellular neural
networks: theory, Proc. IEEE Int Workshop Cellular Neural Networks
Appl.(1996) 181-186.
[29] T. Yang, L. Yang,C. Wu, L. Chua, Fuzzy cellular neural networks:
applications, Proc. IEEE Int. Workshop on Cellular Neural Neworks
Appl. (1996)225-230.
[30] T. Huang, Exponential stability of fuzzy cellular neural networks with
distributed delay, Phys. Lett. A 351(2006) 48-52.
[31] T. Huang, Exponential stability of delayed fuzzy cellular neural networks
with diffusion, Chaos Solitons Fractals 31 (2007) 658-664.
[32] Q. Zhang and R. Xiang, Global asymptotic stability of fuzzy cellular
neural networks with time-varying delays, Phy. Lett. A 371 (2008)
3971-3977.
[33] Q. Zhang and W. Luo, Global Exponential Stability and Periodic
Solutions of FCNNs with Constant Delays and Time-varying Delays,
Proceeding of 2009 International Joint Conference on Computational
Sciences and Optimization, Volume 2,659-662.
[34] Y. Wu and Q. Zhang, Global Exponential Stability of Fuzzy Cellular
Neural Networks with Variable Delays and Distributed Delays, Proceeding
of the 6th Conference of Biomathematics,2008, 695-699.
[35] K. Yuan,J. Cao and J. Deng, Exponential stability and periodic solutions
of fuzzy cellular neural networks with time-varying delays, Neurocomputing
69 (2006) 1619-1627.
[36] J. Cao and Q. Jiang, An analysis of periodic solutions of bi-directional
associative memory networks with time-varying delays, Physics Lett.
A 330(2004)203-213.
[1] B. Kosto, Adaptive bi-directional associative memories, Appl. Opt. 26
(1987) 4947-4960.
[2] B. Kosto, Bi-directional associative memories, IEEE Trans.Syst. Man
Cybernet.18(1988)49-60.
[3] B. Kosto, Neural Networks and Fuzzy Systems:A Dynamical Systems
Approach to Machine Intelligence, Prentice-Hall, Englewood Cliffs,
NJ, 1992,38.
[4] K. Gopalsmy and X. Z. He, Delay-independent stability in bi-directional
associative memory networks, IEEE Trans. Neural Networks 5 (1994)
998-1002.
[5] J. Cao and L. Wang, Periodic oscillatory solution of bidirectional
associative memory networks with delays, Phys. Rev. E 61 (2000)
1825-1828.
[6] B. Liu and L. Huang, Global exponential stability of BAM neural
networks with recent-history distributed delays and impulse, Neurocomputing
69 (2006) 2090-2096.
[7] J. Cao and L. Wang, Exponential stability and periodic oscilatory
solution in BAM networks with delays, IEEE Trans. Neural Networks
13 (2002) 457-463.
[8] H. Zhao, Global exponential stability of bidirectional associative memory
neural networks with distributed delays, Phys. Lett. A 297 (2002) 182-
190.
[9] J. Zhang and Y. Yang, Global stability analysis of bidirectional
associative memory neural networks with time delay, Int.J.Ciruit
Theor.Appl.29(2001)185-196.
[10] X. F. Liao, K.W. Wong and S. Z. Yang, Convergence dynamics of hybrid
bidirectional associative memory neural networks with distributed delays,
Phys. Lett. A 316 (2003) 55-64.
[11] X. F. Liao and J. B. Yu, Qualitative analysis of bi-directional associative
memory with time delay, Int. J. Circ. Theory Appl. 26(1998)219-229.
[12] J. Cao and Q. Jiang, An analysis of periodic solutions of bi-directional
associative memory networks with time-varying delays, Phys. Lett. A
330 (2004) 203-213.
[13] A. Chen, J. Cao and L. Huang, Exponential stability of BAM neural
networks with transmission delays, Neurocomputing 57 (2004) 435-454.
[14] A. Chen, L. Huang, J. Cao, Existence and stability of almost periodic
solution for BAM neural networks with delays, Appl. Math. Comput.
137 (2003) 177-193.
[15] A. Chen, L. Huang, Z. Liu and J. Cao, Periodic bidirectional
associative memory neural networks with distributed delays, Journal
of Math. Analys. and Appl. 317 (2006) 80-102.
[16] Z. Liu, A. Chen, J. Cao and L. Huang, Existence and global
exponential stability of almost periodic solutions of BAM neural networks
with continuously distributed delays, Phys. Lett. A 319 (2003) 305-316.
[17] S. J. Guo, L. H. Huang, B. X. Dai and Z. Z. Zhang, Global existence
of periodic solutions of BAM neural networks with variable coefficients,
Phys. Lett. A 317(2003) 97-106.
[18] J. Cao, A set of stability criteria for delayed cellular neural networks,
IEEE Trans. Circuits Systems I 48 (4) (2001) 494-498.
[19] J. Cao, Global stability conditions for delayed CNNs, IEEE Trans.
Circuits Systems I 48(2001) 1330-1333.
[20] J. Cao and J. Wang, Global asymptotic stability of general class
of recurrent neural networks with time-varying delays, IEEE Trans.
Circuits Systems I 50 (2003)34-44.
[21] J. Cao, New results concerning exponential stability and periodic
solutions of delayed cellular neural networks, Phys. Lett. A 307 (2003)
136-147.
[22] J. Cao and J. Wang, Absolute exponential stability of recurrent neural
networks with Lipschitz-continuous activation functions and time delays,
Neural Networks 17 (2004) 379-390.
[23] J. Cao and J. Wang, Global exponential stability and periodicity of
recurrent neural networks with time delays, IEEE Trans. Circuits
Systems I 52 (2005)920-931.
[24] J. Cao and D. W. C. Ho, A general framework for global asymptotic
stability analysis of delayed neural networks based on LMI approach,
Chaos Solitons Fractals 24 (2005) 1317-1329.
[25] J. Cao, D. Huang and Y. Qu, Global robust stability of delayed
recurrent neural networks , Chaos Solitons Fractals 23 (2005)221-=229.
[26] Q. Song, Z. Zhao and Y. Li, Global exponential stability of BAM neural
networks with distributed delays and reactionCdiffusion terms, Phys Lett.
A 335(2005)213-225.
[27] T. Yang and L. B. Yang, The global stability of fuzzy cellular neural
networks, IEEE Trans. Circ. Syst. I 43(1996)880-883.
[28] T. Yang,L. B.Yang.,C. W.Wu and L. O.Chua, Fuzzy cellular neural
networks: theory, Proc. IEEE Int Workshop Cellular Neural Networks
Appl.(1996) 181-186.
[29] T. Yang, L. Yang,C. Wu, L. Chua, Fuzzy cellular neural networks:
applications, Proc. IEEE Int. Workshop on Cellular Neural Neworks
Appl. (1996)225-230.
[30] T. Huang, Exponential stability of fuzzy cellular neural networks with
distributed delay, Phys. Lett. A 351(2006) 48-52.
[31] T. Huang, Exponential stability of delayed fuzzy cellular neural networks
with diffusion, Chaos Solitons Fractals 31 (2007) 658-664.
[32] Q. Zhang and R. Xiang, Global asymptotic stability of fuzzy cellular
neural networks with time-varying delays, Phy. Lett. A 371 (2008)
3971-3977.
[33] Q. Zhang and W. Luo, Global Exponential Stability and Periodic
Solutions of FCNNs with Constant Delays and Time-varying Delays,
Proceeding of 2009 International Joint Conference on Computational
Sciences and Optimization, Volume 2,659-662.
[34] Y. Wu and Q. Zhang, Global Exponential Stability of Fuzzy Cellular
Neural Networks with Variable Delays and Distributed Delays, Proceeding
of the 6th Conference of Biomathematics,2008, 695-699.
[35] K. Yuan,J. Cao and J. Deng, Exponential stability and periodic solutions
of fuzzy cellular neural networks with time-varying delays, Neurocomputing
69 (2006) 1619-1627.
[36] J. Cao and Q. Jiang, An analysis of periodic solutions of bi-directional
associative memory networks with time-varying delays, Physics Lett.
A 330(2004)203-213.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51024", author = "Qianhong Zhang and Lihui Yang and Daixi Liao", title = "Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks", abstract = "In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.", keywords = "Fuzzy BAM neural networks, Periodic solution,Global exponential stability, Time-varying delays", volume = "5", number = "3", pages = "264-6", }
