Abstract
In this paper, the quasi-synchronization problem of stochastic memristive neural networks (MNNs) subject to deception attacks is investigated via hybrid impulsive control. Deception attacks in the MNN synchronization model, which involve the attacker attempting to inject some false data into sensor-to-controller channels to destroy the control signal, are investigated from the perspective of network communication security. The attack conditions are described using stochastic variables that obey the Bernoulli distribution. Inspired by existing impulsive differential inequalities, a new inequality is proposed, which is useful for dealing with quasi-synchronization in impulsive systems. Thereafter, sufficient conditions and the error bound are obtained for validating the quasi-synchronization of stochastic MNNs subject to deception attacks based on the proposed inequality and Lyapunov stability theory. In the absence of an attack, the globally complete synchronization problem for stochastic MNNs is investigated. Additionally, the attack effects and their mitigation through control parameter design are discussed. Finally, the simulation results are presented to validate the theoretical analysis.
Similar content being viewed by others
References
Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80 (2008)
Pershin, Y.V., Di Ventra, M.: Massimiliano: Experimental demonstration of associative memory with memristive neural networks. Neural Networks 23(7), 881–886 (2010)
Pedretti, G., Milo, V., Ambrogio, S., Carboni, R., Bianchi, S., Calderoni, A., Ramaswamy, N., Spinelli, A.S., Ielmini, D.: Memristive neural network for on-line learning and tracking with brain-inspired spike timing dependent plasticity. Sci. Rep. 7(1), 5288 (2017)
Guo, Z., Wang, J., Yan, Z.: Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 704–717 (2013)
Lin, H., Wang, C., Sun, Y., Yao, W.: Firing multistability in a locally active memristive neuron model. Nonlinear Dynam. (2020)
Yao, W., Wang, C., Cao, J., Sun, Y., Zhou, C.: Hybrid multisynchronization of coupled multistable memristive neural networks with time delays. Neurocomputing 363, 281–294 (2019)
Chen, C., Li, L., Peng, H., Yang, Y., Mi, L., Zhao, H.: A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. Neural Netw. 123, 412–419 (2020)
Wen, S., Zeng, Z., Huang, T., Meng, Q., Yao, W.: Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1493–1502 (2015)
Singer, W.: Synchronization of cortical activity and its putative role in information processing and learning. Ann. Rev. Physiol. 55(1), 349–374 (1993)
Hoppensteadt, F.C., Izhikevich, E.M.: Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans. Neural Netw. 11(3), 734–738 (2000)
Zhu, S., Bao, H.: Event-triggered synchronization of coupled memristive neural networks. Appl. Math. Comput. 415, 126715 (2022)
Dong, S., Zhu, H., Zhong, S., Shi, K., Liu, Y.: New study on fixed-time synchronization control of delayed inertial memristive neural networks. Appl. Math. Comput. 399, 126035 (2021)
Zhou, C., Wang, C., Sun, Y., Yao, W., Lin, H.: Cluster output synchronization for memristive neural networks. Inform. Sci. 589, 459–477 (2022)
Song, Y., Zeng, Z., Sun, W., Jiang, F.: Quasi-synchronization of stochastic memristor-based neural networks with mixed delays and parameter mismatches. Neural Comput. Appl. 32(9), 4615–4628 (2020)
Fan, Y., Huang, X., Li, Y., Xia, J., Chen, G.: Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: An interval matrix and matrix measure combined method. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2254–2265 (2019)
Ma, F., Gao, X.: Synchronization and quasi-synchronization of delayed fractional coupled memristive neural networks. Neural Process. Lett. 54(3), 1647–1662 (2022)
Ye, D., Shao, Y.: Quasi-synchronization of heterogeneous nonlinear multi-agent systems subject to dos attacks with impulsive effects. Neurocomputing 366, 131–139 (2019)
Zhang, W., Yang, S., Li, C., Zhang, W., Yang, X.: Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control. Neural Netw. 104, 93–103 (2018)
Li, X., Fang, J., Li, H.: Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays. Neurocomputing 267, 396–405 (2017)
Wang, W., Xin, Yu., Luo, X., Kurths, J.: Synchronization control of memristive multidirectional associative memory neural networks and applications in network security communication. IEEE Access 6, 36002–36018 (2018)
Guo, Y., Luo, Y., Wang, W., Luo, X., Ge, C., Kurths, J., Yuan, M., Gao, Y.: Fixed-time synchronization of complex-valued memristive bam neural network and applications in image encryption and decryption. Int. J. Control Autom. Syst. 18(2), 462–476 (2020)
Pal Chowdhury, A., Kulkarni, P., Nazm Bojnordi, M.: Mb-cnn: memristive binary convolutional neural networks for embedded mobile devices. J. Low Power Electron. Appl. 8(4), 38 (2018)
Bai, J., Wu, H., Cao, J.: Secure synchronization and identification for fractional complex networks with multiple weight couplings under dos attacks. Computat. Appl. Math. 41(4), 1–18 (2022)
Liu, J., Xia, J., Tian, E., Fei, S.: Hybrid-driven-based h filter design for neural networks subject to deception attacks. Appl. Math. Comput. 320, 158–174 (2018)
Du, D., Zhang, C., Wang, H., Li, X., Hu, H., Yang, T.: Stability analysis of token-based wireless networked control systems under deception attacks. Inform. Sci. 459, 168–182 (2018)
He, W., Gao, X., Zhong, W., Qian, F.: Secure impulsive synchronization control of multi-agent systems under deception attacks. Inform. Sci. 459, 354–368 (2018)
Zhao, L., Yang, G.-H.: Cooperative adaptive fault-tolerant control for multi-agent systems with deception attacks. J. Franklin Inst. 357(6), 3419–3433 (2020)
Wang, H., Duan, S., Huang, T., Tan, J.: Synchronization of memristive delayed neural networks via hybrid impulsive control. Neurocomputing 267, 615–623 (2017)
Zheng, S., Shao, W.: Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling. Nonlinear Dyn. 73(4), 2343–2352 (2013)
Yang, X., Cao, J., Lu, J.: Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I Regular Papers 59(2), 371–384 (2011)
Guan, Z.H., Liu, Z.W., Feng, G., Wang, Y.W.: Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I: Regular Papers 57(8), 2182–2195 (2010)
Wu, Q., Zhou, J., Xiang, L.: Impulses-induced exponential stability in recurrent delayed neural networks. Neurocomputing 74(17), 3204–3211 (2011)
Yang, X., Yang, Z.: Synchronization of ts fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects. Fuzzy Sets Syst. 235, 25–43 (2014)
Zhang, G., Shen, Y.: Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1431–1441 (2014)
Yuan, M., Wang, W., Wang, Z., Luo, X.: Exponential synchronization of delayed memristor-based uncertain complex-valued neural networks for image protection. IEEE Trans. Neural Netw. Learn. Syst. 32(1), 151–165 (2021)
Wang, W., Jia, X., Luo, X., Kurths, J., Yuan, M.: Fixed-time synchronization control of memristive mam neural networks with mixed delays and application in chaotic secure communication. Chaos Solitons Fractals 126, 85–96 (2019)
Wen, S., Zeng, Z., Huang, T., Zhang, Y.: Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans. Fuzzy Syst. 22(6), 1704–1713 (2013)
Peterson, P.: Unmasking deceptive attacks with machine learning. Comput. Fraud Security 2018(11), 15–17 (2018)
Filippov, A.F.: Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control 5(4), 609–621 (1967)
Aubin, J.-P., Cellina, A.: Differential Inclusions: Set-valued Maps and Viability Theory, vol. 264. Springer Science & Business Media, Berlin (2012)
Xu, Y., Wu, X., Xu, C.: Synchronization of time-varying delayed neural networks by fixed-time control. IEEE Access 6, 74240–74246 (2018)
Fei, Z., Guan, C., Gao, H.: Exponential synchronization of networked chaotic delayed neural network by a hybrid event trigger scheme. IEEE Trans. Neural Netw. Learn. Syst. 29(6), 2558–2567 (2017)
Yang, Z., Xu, D., Xiang, L.: Exponential p-stability of impulsive stochastic differential equations with delays. Phys. Lett. A 359(2), 129–137 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chao, Z., Wang, C. & Yao, W. Quasi-synchronization of stochastic memristive neural networks subject to deception attacks. Nonlinear Dyn 111, 2443–2462 (2023). https://doi.org/10.1007/s11071-022-07925-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-07925-2