New PTH Moment Stable Criteria of Stochastic Neural Networks
In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.
[1] L. Sheng and H.Z. Yang. Exponential synchronization of a class of
neural networks with mixed time-varying delays and impulsive effects.
Neurocomputing, 7: 3666-3674.
[2] O.M. Kwon and J.H. Park. Exponential stability for uncertain cellular
neural networks with discrete and distributed time-varying delays. Appl.
Math. Comput, 203: 813-823.
[3] Y.H. Xia, Z.K. Huang and M.A. Han. Exponential p-stability of delayed
Cohen-Grossberg-type BAM neural networks with impulses. Chaos, Solitons
and Fractals, 38: 806-818.
[4] P. Balasubramaniam and R. Rakkiyappan. Global asymptotic stability of
stochastic recurrent neural networks with multiple discrete delays and
unbounded distributed delays. Appl. Math. Comput, 204: 680-686.
[5] P. Balasubramaniam and R. Rakkiyappan. LMI conditions for global
asymptotic stability results for neutral-type neural networks with distributed
time delays. Appl. Math. Comput, 204: 317-324.
[6] J.J. Yu et al. Simplified exponential stability analysis for recurrent neural
networks with discrete and distributed time-varying delays. Appl. Math.
Comput, 205:465-474.
[7] S. Haykin. Neural Networks. Prentice-Hall, NJ.
[8] C.X. Huang, Y.G. He, P. Chen. Dynamic Analysis of Stochastic Recurrent
Neural Networks. Neural. Process. Lett, 27: 267-276.
[9] L. Wan, J.H. Sun. Mean square exponential stability of stochastic delayed
Hopfield neural networks. Phys. Lett. A,343, : 306-318.
[10] X.Y. Lou, B.T. Cui. Delay-dependent stochastic stability of delayed
Hopfield neural networks with Markovian jump parameters. J. Math.
Anal. Appl, 328: 316-326.
[11] L.S. Wang, Z. Zhang and Y.F. Wang. Stochastic exponential stability of
the delayed reactionCdiffusion recurrent neural networks with Markovian
jumping parameters. Phys. Lett. A, 18: 3201-3209.
[12] Z.D. Wang, Y.R. Liu, L. Yu and X.H. Liu. Exponential stability of
delayed recurrent neural networks with Markovian jumping parameters.
Phys. Lett. A, 4: 346-352.
[13] E.W. Zhu et al. pth Moment Exponential Stability of Stochastic Cohen-
Grossberg Neural Networks With Time-varying Delays. Neural. Process.
Lett, 26: 191-200.
[14] J. Randjelovic, S. Jankovic. On the pth moment exponential stability
criteria of neutral stochastic functional differential equations. J. Math.
Anal. Appl, 326 :266-280.
[15] Y.H. Sun, J.D. Cao. pth moment exponential stability of stochastic
recurrent neural networks with time-varying delays, Nonlinear Anal.
realword, 8: 1171-1185.
[16] C.X. Huang et al. pth moment stability analysis of stochastic recurrent
neural networks with time-varying delays. Inf. Sci, 178: 2194-2203.
[17] S.J. Wu, D. Han and X.Z. Meng. p-Moment stability of stochastic
differential equations with jumps. Appl. Math. Comput, 152: 505-519.
[18] S.J. Wu, X.L. Guo and Y. Zhou. p-moment stability of functional
differential equations with random impulsive. Comput. Math. Appl, 52:
1683-1694.
[19] H.J. Wu, J.T. Sun. p-Moment stability of stochastic differential equations
with impulsive jump and Markovian switching. Automatica, 42: 1753-
1759.
[20] X.R. Mao. Exponential Stability of Stochastic Differential Equations.
Marcel Dekker, NewYork.
[21] X.R. Mao. Stochastic Differential Equations and Applications. Horwood
Publication, Chichester.
[1] L. Sheng and H.Z. Yang. Exponential synchronization of a class of
neural networks with mixed time-varying delays and impulsive effects.
Neurocomputing, 7: 3666-3674.
[2] O.M. Kwon and J.H. Park. Exponential stability for uncertain cellular
neural networks with discrete and distributed time-varying delays. Appl.
Math. Comput, 203: 813-823.
[3] Y.H. Xia, Z.K. Huang and M.A. Han. Exponential p-stability of delayed
Cohen-Grossberg-type BAM neural networks with impulses. Chaos, Solitons
and Fractals, 38: 806-818.
[4] P. Balasubramaniam and R. Rakkiyappan. Global asymptotic stability of
stochastic recurrent neural networks with multiple discrete delays and
unbounded distributed delays. Appl. Math. Comput, 204: 680-686.
[5] P. Balasubramaniam and R. Rakkiyappan. LMI conditions for global
asymptotic stability results for neutral-type neural networks with distributed
time delays. Appl. Math. Comput, 204: 317-324.
[6] J.J. Yu et al. Simplified exponential stability analysis for recurrent neural
networks with discrete and distributed time-varying delays. Appl. Math.
Comput, 205:465-474.
[7] S. Haykin. Neural Networks. Prentice-Hall, NJ.
[8] C.X. Huang, Y.G. He, P. Chen. Dynamic Analysis of Stochastic Recurrent
Neural Networks. Neural. Process. Lett, 27: 267-276.
[9] L. Wan, J.H. Sun. Mean square exponential stability of stochastic delayed
Hopfield neural networks. Phys. Lett. A,343, : 306-318.
[10] X.Y. Lou, B.T. Cui. Delay-dependent stochastic stability of delayed
Hopfield neural networks with Markovian jump parameters. J. Math.
Anal. Appl, 328: 316-326.
[11] L.S. Wang, Z. Zhang and Y.F. Wang. Stochastic exponential stability of
the delayed reactionCdiffusion recurrent neural networks with Markovian
jumping parameters. Phys. Lett. A, 18: 3201-3209.
[12] Z.D. Wang, Y.R. Liu, L. Yu and X.H. Liu. Exponential stability of
delayed recurrent neural networks with Markovian jumping parameters.
Phys. Lett. A, 4: 346-352.
[13] E.W. Zhu et al. pth Moment Exponential Stability of Stochastic Cohen-
Grossberg Neural Networks With Time-varying Delays. Neural. Process.
Lett, 26: 191-200.
[14] J. Randjelovic, S. Jankovic. On the pth moment exponential stability
criteria of neutral stochastic functional differential equations. J. Math.
Anal. Appl, 326 :266-280.
[15] Y.H. Sun, J.D. Cao. pth moment exponential stability of stochastic
recurrent neural networks with time-varying delays, Nonlinear Anal.
realword, 8: 1171-1185.
[16] C.X. Huang et al. pth moment stability analysis of stochastic recurrent
neural networks with time-varying delays. Inf. Sci, 178: 2194-2203.
[17] S.J. Wu, D. Han and X.Z. Meng. p-Moment stability of stochastic
differential equations with jumps. Appl. Math. Comput, 152: 505-519.
[18] S.J. Wu, X.L. Guo and Y. Zhou. p-moment stability of functional
differential equations with random impulsive. Comput. Math. Appl, 52:
1683-1694.
[19] H.J. Wu, J.T. Sun. p-Moment stability of stochastic differential equations
with impulsive jump and Markovian switching. Automatica, 42: 1753-
1759.
[20] X.R. Mao. Exponential Stability of Stochastic Differential Equations.
Marcel Dekker, NewYork.
[21] X.R. Mao. Stochastic Differential Equations and Applications. Horwood
Publication, Chichester.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54948", author = "Zixin Liu and Huawei Yang and Fangwei Chen", title = "New PTH Moment Stable Criteria of Stochastic Neural Networks", abstract = "In this paper, the issue of pth moment stability of a class of stochastic neural networks with mixed delays is investigated. By establishing two integro-differential inequalities, some new sufficient conditions ensuring pth moment exponential stability are obtained. Compared with some previous publications, our results generalize some earlier works reported in the literature, and remove some strict constraints of time delays and kernel functions. Two numerical examples are presented to illustrate the validity of the main results.
", keywords = "Neural networks, stochastic, PTH moment stable, time varying delays, distributed delays.", volume = "5", number = "8", pages = "1245-6", }
