Abstract
In this article, we have considered a mathematical model of a neural network. The model is characterised by a delay difference equation with stochastic perturbations. We have proved the condition of asymptotic stability behaviour of the trivial solution of s multiple-delay model with stochastic terms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Elaydi S (2008) An introduction to difference equations, 3rd edn. Springer International Edition, First Indian Reprint
Mickens RE (2015) Difference equations theory, applications and advance topics, 3rd edn. CRC Press, USA
Agarwal R P, Wong PJY (1997) Advanced topics in difference equations. Kluwer Academic Publishers
Appleby J, Mao X, Rodkina A (2006) On Stochastic stabilization of difference equations. Dynamics of Continuous and Discrete Systems 15(3):843–857
Ensari T, Arik S (2005) Global stability analysis of neural networks multiple time varying delays. IEEE Trans Autom Control 50(11):1781–1785
Elizabeth S, Nirmal Veena S (2017) Study on asymptotic stabilization of non-linear delay difference equations. Int J Difference Equations 12(1):15–20
Ammar B, Cherif F, Alimi AM (2012) Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural Networks wiath time-varying coefficients and mixed delays. IEEE Trans Neural Netw Learn Syst 23(1):109–118
Cao J, Zhou D (1998) Stability analysis of delayed cellular neural networks. Neural Netw 51(11):1601–1605
Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865
Huang T, Li C, Duan S, Starzyk J (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875
Liu Z, Zhang H, Zhang Q (2010) Novel stability analysis of recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans Neural Netw 21(11):1710–1718
Mou S, Gao H, Lam J, Qiang W (2008) A new criterian of delay-dependent asymptotic stability for Hopfield neural networks with time-delay. IEEE Trans Neural Netw 19(3):532–535
Stoica A-M, Yaesh I (2008) Markovian jump delayed Hopfield networks with multiplicative noise. Automatica 44(8):2157–2162
Liu B, Lu W, Chen T (2011) Generalized Halanay inequalities and their applications to neural networks with unbounded time-varying delays. IEEE Trans Neural Netw 22(9):1508–1513
Liu X, Teo KL, Xu B (2005) Exponential stability of impulsive high order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 16(6):1329–1339
Xu S, Lam J (2006) A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Netw 19(1):76–83
Yu G-J, Lu C-Y, Tasi JS-H, Su TJ, Liu BD (2003) Stability of cellular neural networks with time-varying delay. IEEE Trans Circuits Syst Part I, 50(5):677–679
Rodkina A, Schurz H (2004) A Theorem on asymptotic stability of solutions of non-linear stochastic difference equations with Volterra type noise. SACTA 6(1):23–34
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Lakshmi, M., Das, R. (2021). Asymptotic Stability of Neural Network System with Stochastic Perturbations. In: Mandal, J.K., Mukhopadhyay, S., Unal, A., Sen, S.K. (eds) Proceedings of International Conference on Innovations in Software Architecture and Computational Systems. Studies in Autonomic, Data-driven and Industrial Computing. Springer, Singapore. https://doi.org/10.1007/978-981-16-4301-9_6
Download citation
DOI: https://doi.org/10.1007/978-981-16-4301-9_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-4300-2
Online ISBN: 978-981-16-4301-9
eBook Packages: Computer ScienceComputer Science (R0)