Abstract
We consider the global existence of solutions and mean-square exponential input-to-state stability for a class of stochastic delayed Cohen-Grossberg neural networks without global Lipschitz condition. Under local Lipschitz condition, we find new sufficient conditions that ensure the solutions of given neural networks exist globally and are mean-square exponentially input-to-state stable. Furthermore, we highlight the advantages of our novel results by comparing with the results in Zhou et al. (2015) as well as a numerical example.
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References
Cohen MA, Grossberg S (1983) Absolute stability of global pattern formulation and parallel memory storage by competitive neural net networks. IEEE Trans Syst Man Cybern SMC 13:815–826
Wang Z, Liu Y, Li M, Liu X (2006) Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 17:814–820
Rakkiyappan R, Balasubramaniam P (2009) Dynamic analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays. Nonlinear Anal Hybrid Syst 3:408–417
Fu X, Li X (2011) LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 16:435–454
Su W, Chen Y (2009) Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed timevarying delays. Commun Nonlinear Sci Numer Simul 14:520–528
Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370
Zhu Q, Li X (2012) Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks. Fuzzy Set Syst 203:74–94
Wang C, Kao Y, Yang G (2012) Exponential stability of impulsive stochastic fuzzy reaction-diffusion Cohen-Grossberg neural networks with mixed delays. Neurocomputing 89:55–63
Li T, Song A, Fei S (2009) Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays. Neurocomputing 73:542–551
Song Q, Wang Z (2008) Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Physica A 387:3314–3326
Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21:1314–1325
Li B, Xu DY (2012) Existence and exponential stability of periodic solution for impulsive Cohen-Grossberg neural networks with time-varying delays. Appl Math Comput 219:2506–2520
Wang XH, Guo QY, Xu DY (2009) Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays. Math Comput Simul 79:1698–1710
Yang T, Xiong Z, Yang C (2019) Analysis of exponential stability for neutral stochastic Cohen-Grossberg neural networks with mixed delays. Discrete Dyn Nat Soc 2019:4813103
Xu C, Li P (2017) Pth moment exponential stability of stochastic fuzzy Cohen-Grossberg neural networks with discrete and distributed delays. Nonlinear Anal Model Control 22:531–544
Zhou W, Teng L, Xu D (2015) Mean-square exponentially input-to-state stability of stochastic Cohen-Grossberg neural networks with time-varying delays. Neurocomputing 153:54–61
Zhu Q, Cao J, Rakkiyappan R (2015) Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays. Nonlinear Dynam 79:1085–1098
Zhu Q, Cao J (2014) Mean-square exponential input-to-state stability of stochastic delayed neural networks. Neurocomputing 131:157–163
Wang W, Chen W (2021) Mean-square exponential input-to-state stability of stochastic inertial neural networks. Adv Differ Equ 2021:430
Wang W, Gong S, Chen W (2018) New result on the mean-square exponential input-to-state stability of stochastic delayed recurrent neural networks. Syst Sci Control Eng 6(1):501–509
Wang W, Chen W (2022) Mean-square exponential stability of stochastic inertial neural networks. Internat J Control 95(4):1003–1009
Li Z, Liu L, Zhu Q (2016) Mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching based on vector Lyapunov functions. Neural Netw 84:39–46
Song Y, Sun W, Jiang F (2016) Mean-square exponential input-to-state stability for neutral stochastic neural networks with mixed delays. Neurocomputing 205:195–203
Fu Q, Cai J, Zhong S (2019) Input-to-state stability of discrete-time memristive neural networks with two delay components. Neurocomputing 329:1–11
Shu Y, Liu X, Wang F, Qiu S (2018) Exponential input-to-state stability of stochastic neural networks with mixed delays. Int J Mach Learn & Cyber 9:807–819
Liu D, Zhu S, Chang W (2017) Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay. Int J Syst Sci 48:1966–1977
Zhu Q (2019) Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Control 64(9):3764–3771
Yang X, Wang H, Zhu Q (2022) Event-triggered predictive control of nonlinear stochastic systems without put delay. Automatica 140:110230
Khasminskii R (2012) Stochastic stability of differential equations. Springer, Berlin Heidelberg
Mao X (1997) Stochastic differential equations and applications. Horwood Publishing, Chichester, UK
Acknowledgements
This work was supported by the Natural Scientific Research Fund of Zhejiang Provincial of China (grant no. LY18A010019, LY16A010018).
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Wang, W. Further Results on Mean-Square Exponential Input-to-State Stability of Stochastic Delayed Cohen-Grossberg Neural Networks. Neural Process Lett 55, 3953–3965 (2023). https://doi.org/10.1007/s11063-022-10974-8
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DOI: https://doi.org/10.1007/s11063-022-10974-8