Stability analysis for time-delayed neural networks driven by <i>G</i>−Brownian motion

DING Chang; SHEN Bo

doi:10.12299/jsues.22-0014

Volume 36 Issue 2

Jun. 2022

Turn off MathJax

Article Contents

Article Navigation > Journal of Shanghai University of Engineering Science > 2022 > 36(2): 130-138

DING Chang, SHEN Bo. Stability analysis for time-delayed neural networks driven by G−Brownian motion[J]. Journal of Shanghai University of Engineering Science, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014

Citation:

DING Chang, SHEN Bo. Stability analysis for time-delayed neural networks driven by G−Brownian motion[J]. Journal of Shanghai University of Engineering Science, 2022, 36(2): 130-138. doi: 10.12299/jsues.22-0014

Citation:

PDF( 798 KB)

Stability analysis for time-delayed neural networks driven by G−Brownian motion

doi: 10.12299/jsues.22-0014

DING Chang^a
,,
SHEN Bo^{b
,
,}

a.
College of Science
b.
College of Information Science and Technology, Donghua University, Shanghai 201620, China

Received Date: 2022-01-21
Accepted Date: 2022-01-21

Available Online: 2022-11-16

Publish Date: 2022-06-30

Abstract

Abstract

The stability problem was investigated for a class of time-delayed neural networks driven by G−Brownian motion (G−DNNs). The random noise does not always obeys a normal distribution, in order to better describe the actual situation, G−Brownian motion was used to describe the noise, and the influence of discrete-time observations of G-Brownian motion noise on the stability of time-delayed neural networks was analyzed. For exponentially stable time-delayed neural networks, the random noise driven by G-Brownian motion was introduced, the upper bound of random noise intensity was given by using G−random analysis theory, Gronwall inequality, and Borel-Cantelli lemma, and when the noise intensity was less than the upper bound, the stability speed of stochastic delayed recurrent neural networks was faster than that of the original. The stability of stochastic delayed recurrent neural networks was further analyzed in the case of discrete-time noise. By using the G−Itô formula, scaling technique, and some basic inequalities, the upper bound was obtained for the discrete-time step size of the noise and the stability of the stochastic delayed recurrent neural networks was further accelerated. The validity of theoretical results was verified by an example.
- time-delayed neural networks,
- exponential decay,
- G−Brownian motion,
- noise

FullText(HTML)

References(22)

References

[1]	GOPALSAMY K, LEUNG I. Delay induced periodicity in a neural netlet of excitation and inhibition[J] . Physica D:Nonlinear Phenomena,1996,89(3/4):395 − 426.
[2]	PHAM J, PAKDAMAN K, VIBERT J. Noise-induced coherent oscillations in randomly connected neural networks[J] . Stochastic Processes and Their Applicat-ions,1998,58(3):3610 − 3622.
[3]	LIAO X X, WANG J. Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays[J] . IEEE Transactions on Circuits and Systems I:Regular Papers,2003,50(2):268 − 274. doi: 10.1109/TCSI.2002.808213
[4]	LIU Y R, WANG Z D, LIU X H. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays[J] . Neural Networks,2006,19(5):667 − 675. doi: 10.1016/j.neunet.2005.03.015
[5]	LI D, ZHU Q X. Comparison principle and stability of stochastic delayed neural networks with Markovian switching[J] . Neurocomputing,2014,123(10):436 − 442.
[6]	CAO J D, YUAN K, Li H X. Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays[J] . IEEE Transactions on Neural Networks,2006,17(6):1646 − 1651. doi: 10.1109/TNN.2006.881488
[7]	SHEN Y, WANG J. Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances[J] . IEEE Transactions on Neural Networks and Learning Systems,2012,23(1):87 − 96. doi: 10.1109/TNNLS.2011.2178326
[8]	ZHU S, SHEN Y, CHEN G C. Noise suppress or express exponential growth for hybrid Hopfield neural networks[J] . Physics Letters A,2010,374(19/20):2035 − 2043. doi: 10.1016/j.physleta.2010.03.005
[9]	LIU L, SHEN Y. Noise suppresses explosive solutions of differential systems with coefficients satisfying the poly-nomial growth condition[J] . Automatica,2012,8(4):619 − 624.
[10]	ZHU S, YANG Q Q, SHEN Y. Noise further expresses exponential decay for globally exponentially stable time-varying delayed neural networks[J] . Neural Networks,2016,77:7 − 13. doi: 10.1016/j.neunet.2016.01.012
[11]	LI X P, LIN X Y, LIN Y Q. Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion[J] . Journal of Mathematical Analysis and Applications,2016,439(1):235 − 255. doi: 10.1016/j.jmaa.2016.02.042
[12]	REN Y, YIN W S, SAKTHIVEL R. Stabilization of stochastic differential equations driven by G-Brownian motion with feedback control based on discrete-time state observation[J] . Automatica,2018,95:146 − 151. doi: 10.1016/j.automatica.2018.05.039
[13]	CHEN Z, YANG D D. Stability analysis of Hopfield neural networks with unbounded delay driven by G-Brownian motion[J] . International Journal of Control,2021,95(1):11 − 21.
[14]	LI Y X, REN Y. Stability for stochastic reaction–diffusion systems driven by G-Brownian motion [J]. International Journal of Control, 2021. DOI: 10.1080/00207179.2021.1885742.
[15]	DUAN P J. Existence and exponential stability of almost pseudo Automorphic solution for neutral stochastic evolution equations driven by G-Brownian motion[J] . Filomat,2020,34(4):1075 − 1092. doi: 10.2298/FIL2004075D
[16]	LI Y Y, FEI W Y, DENG S N. Delay feedback stabilisation of stochastic differential equations driven by G-Brownian motion [J]. International Journal of Control, 2021. DOI: 10.1080/00207179.2021.1916077.
[17]	YAO S H, ZONG X F. Delay-dependent stability of a class of stochastic delay systems driven by G-Brownian motion[J] . IET Control Theory and Applications,2020,14(6):836 − 842.
[18]	YIN W S, CAO J D, REN Y. Quasi-sure exponential stabilization of stochastic systems induced by G-Brownian motion with discrete time feedback control[J] . Journal of Mathematical Analysis and Applications,2019,474(1):276 − 289. doi: 10.1016/j.jmaa.2019.01.045
[19]	MAO X R. Stability and stabilization of stochastic dif-ferential delay equations[J] . IET Control Theory and Applications,2007,1(6):1551 − 1566. doi: 10.1049/iet-cta:20070006
[20]	PENG S G. G-Expectation, G-Brownian motion and related stochastic calculus of Itô type[J] . Stochastic Analysis and Applications,2006,2(4):541 − 567.
[21]	LI X P, PENG S G. Stopping times and related Itô’s calculus with G-Brownian motion[J] . Stochastic Processes and Their Applications,2011,121(7):1492 − 1508. doi: 10.1016/j.spa.2011.03.009
[22]	GAO F Q. Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion[J] . Stochastic Processes and Their Applications,2009,119(10):3356 − 3382. doi: 10.1016/j.spa.2009.05.010