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Article

Maharajan, Chinnamuniyandi ; Sowmiya, Chandran ; Xu, Changjin
Delay dependent complex-valued bidirectional associative memory neural networks with stochastic and impulsive effects: An exponential stability approach. (English). Kybernetika, vol. 60 (2024), issue 3, pp. 317-356
MSC: 34Dxx, 92B20, 93Exx | DOI: 10.14736/kyb-2024-3-0317
Keywords:
Complex-valued neural networks; Linear matrix inequality; Lyapunov–Krasovskii functional; BAM neural networks; Exponential stability; Impulsive effects; Stochastic noise; discrete delays; distributed delays; leakage delays; mixed time delays
Summary:
This paper investigates the stability in an exponential sense of complex-valued Bidirectional Associative Memory (BAM) neural networks with time delays under the stochastic and impulsive effects. By utilizing the contracting mapping theorem, the existence and uniqueness of the equilibrium point for the proposed complex-valued neural networks are verified. Moreover, based on the Lyapunov - Krasovskii functional construction, matrix inequality techniques and stability theory, some novel time-delayed sufficient conditions are attained in linear matrix inequalities (LMIs) form, which ensure the exponential stability of the trivial solution for the addressed neural networks. Finally, to illustrate the superiority and effects of our theoretical results, two numerical examples with their simulations are provided via MATLAB LMI control toolbox.
References:
[1] Aouiti, C., Assali, E. A., Gharbia, I. B., Foutayeni, Y. E.: Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations. Neurocomputing 357 (2019), 292-309. DOI  | MR 4083491
[2] Chen, X., Song, Q., Liu, Y., Zhao, Z.: Global $\mu$-stability of impulsive complex-valued neural networks with leakage delay and mixed delays. Abstract Appl. Anal. 12 (2014), 1-14. DOI  | MR 3216046
[3] Chen, X., Zhao, Z., Song, Q., Hu, J.: Multistability of complex-valued neural networks with time-varying delays. Appl. Math. Comput. 294 (2017), 18-35. DOI  | MR 3558258
[4] Duan, Q., Park, J., Wu, Z.: Exponential state estimator design for discrete-time neural networks with discrete and distributed time-varying delays. Complexity 20 (2014), 38-48. DOI  | MR 3262755
[5] Kumar, T. G., Ali, M. S., Priya, B., Gokulakrishnan, V., Kauser, S. A.: Impulsive effects on stochastic bidirectional associative memory neural networks with reaction-diffusion and leakage delays. Int. J. Computer Math. 99 (2022), 8, 1669-1686. DOI  | MR 4440030
[6] Gholami, Y.: Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional. Adv. Differ. Eqns, 112 (2021). DOI  | MR 4217062
[7] Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers, Dordrecht 1992. MR 1163190
[8] Gu, K.: A integral inequality in the stability problem of time-delay systems. In: Proc. 39th IEEE Conference on Decision Control, Sydney 3 (200), pp. 2805-2810. DOI 
[9] Haykin, S.: Neural Networks. Prentice Hall, New Jersey 1999.
[10] Ho, D. W. C., Liang, J., Lam, J.: Global exponential stability of impulsive highorder BAM neural networks with time-varying delays. Neural Networks 19 (2006), 10, 1581-1590. DOI  | MR 2111863
[11] Hu, J., Tan, H., Zeng, C.: Global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. Neurocomputing 416 (2020), 8, 1-11. DOI  | MR 4034008
[12] Hu, J., Wang, J.: Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans. Neur. Netw. Learn. Systems 23 (2012), 853-865. DOI 
[13] Huo, N., Li, B., Li, Y.: Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays. AIMS Math. 7 (2022), 3, 3653-3679. DOI  | MR 4347881
[14] Hymavathi, M., Muhiuddin, G., Ali, M. S., Jehad, F., Al-Amri, Gunasekaran, N., Vadivel, R.: Global exponential stability of Fractional order complex-valued neural networks with leakage delay and mixed time varying delays. Fractal and Fractional 6 (2022), 3. DOI  | MR 4209580
[15] Ji, M. D., He, Y., Wu, M., Zhang, C. K.: New exponential stability criterion for neural networks with time-varying delay. In Proc. 33rd Chinese control conference; Nanjing 2014, pp. 6119-6123. DOI 
[16] Ji, M. D., He, Y., Wu, M., Zhang, C. K.: Further results on exponential stability of neural networks with time-varying delay. Appl. Math. Comput. 256 (2015), 175-182. DOI  | MR 3316058
[17] Jia, S., Chen, Y.: Global exponential asymptotic stability of RNNs with mixed asynchronous time-varying delays. Adv. Diff. Eqns 200 (2020). DOI  | MR 4095855
[18] Kosko, B.: Adaptive bi-directional associative memories. Appl. Optim. 26 (1987), 4947-4960. DOI  | MR 0931862
[19] Kosko, B.: Bidirectional associative memories. IEEE Trans. System Man Cybernet. 18 (1988), 49-60. DOI  | MR 0931862
[20] Li, B., Liu, F., Song, Q., Zhang, D., Qiu, H.: State estimation of complex-valued neural networks with leakage delay: A dynamic event-triggered approach. Neurocomputing 520 (2023), 230-239. DOI 
[21] Li, B., Tang, B.: New stability criterion for Fractional-order Quaternion-valued neural networks involving discrete and leakage delays. J. Math. Article ID 9988073 (2021), 20 pages. DOI  | MR 4271429
[22] Li, C., Lian, J., Wang, Y.: Stability of switched memristive neural networks with impulse and stochastic disturbance. Neurocomputing {\mi275} (2018), 2565-2573. DOI 
[23] Li, C., Li, C., Liao, X., Huang, T.: Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74 (2011), 1541-1550. DOI 
[24] Li, D., Wang, X., Xu, D.: Existence and global image exponential stability of periodic solution for impulsive stochastic neural networks with delays. Nonlinear Anal.: Hybrid Sys. 6 (2012), 847-858. MR 2917455
[25] Li, X., Bohner, M., Wang, C.: Impulsive differential equations: Periodic solutions and applications. Automatica 52 (2015), 173-178. DOI  | MR 3310827
[26] Li, X., Song, S.: Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans. Automat. Control 62 (2017), 1, 406-411. DOI  | MR 3598021
[27] Li, X., Zhang, X., Song, S.: Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76 (2017), 378-382. DOI  | MR 3590588
[28] Liu, X., Chen, T.: Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans. Neural Netw. Learn. Sys. 23 (2015), 3, 593-606. DOI  | MR 3465659
[29] Maharajan, C., Raja, R., Cao, J., Rajchakit, G., Alsaedi, A.: Novel results on passivity and exponential passivity for multiple discrete delayed neutral-type neural networks with leakage and distributed time-delays. Chaos, Solitons Fractals 115 (2018), 268-282. DOI  | MR 3862766
[30] Maharajan, C., Raja, R., Cao, J., Rajchakit, G.: Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense. J. Frankl. Inst. 355 (2018), 11, 4727-4754. DOI  | MR 3807164
[31] Maharajan, C., Sowmiya, C.: Exponential stability of delay dependent neutral-type descriptor neural networks with uncertain parameters. Franklin Open 5 (2023), 100042. DOI 
[32] Maharajan, C., Sowmiya, C., Xu, C. J.: Fractional order uncertain BAM neural networks with mixed time delays: An existence and Quasi-uniform stability analysis. J. Intel. Fuzzy Sys. 46 2024, 2, 4291-4313. DOI 
[33] Mao, X., Wang, X., Qin, H.: Stability analysis of quaternion-valued BAM neural networks fractional-order model with impulses and proportional delays. Neurocomputing 509 (2022), 206-220. DOI 
[34] Ou, W., Xu, C. J., Cui, Q., Liu, Z., Pang, Y., Farman, M., Ahmad, S., Zeb, A.: Mathematical study on bifurcation dynamics and control mechanism of tri-neuron BAM neural networks including delay. Math. Meth. Appl. Sci. (2023), 1-25. DOI 
[35] Park, J., Kwon, O.: Global stability for neural networks of neutral-type with interval time-varying delays. Chaos, Solitons Fractals 41 (2009), 1174-1181. DOI  | MR 2537632
[36] Rajchakit, G., Sriraman, R.: Robust passivity and stability analysis of uncertain complex-valued impulsive neural networks with time-varying delays. Neur. Proces. Lett. 53 (2021), 581-606. DOI 
[37] Rakkiyappan, R., Velmurugan, G., Li, X.: Complete stability analysis of complexvalued neural networks with time delays and impulses. Neur. Proces. Lett. 41 (2015), 435-468. DOI 
[38] Ren, H., Karimi, H. R., Lu, R., Wu, Y.: Synchronization of network systems via aperiodic sampled-data control with constant delay and application to unmanned ground vehicles. IEEE Tans. Industr. Electronics 67 (2020), 6, 4980-4990. DOI 
[39] Samidurai, R., Sriraman, R.: Non-fragile sampled-data stabilization analysis for linear systems with probabilistic time-varying delays. J. Franklin Inst. 356 (2019), 8, 4335-4357. DOI  | MR 3950442
[40] Samidurai, R., Sriraman, R., Zhu, S.: Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach. Int. J. Syst. Sci. 50 (2019), 8, 1609-1625. DOI  | MR 3980682
[41] Shao, S., Du, B.: Global asymptotic stability of competitive neural networks with reaction-diffusion terms and mixed delays. Symmetry 14 ID 2224 (2022), 1-11. DOI 
[42] Song, Q., Shu, H., Zhao, Z., Liu, Y., Alsaadi, F. E.: Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244 (2017), 33-41. DOI 
[43] Song, Q., Yang, L., Liu, Y., Alsaadi, F.: Stability of quaternion-valued neutral-type neural networks with leakage delay and proportional delays. Neurocomputing 521 (2023), 191-198. DOI 
[44] Song, Q., Zhao, Z., Liu, Y.: Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159 (2015), 96-104. DOI 
[45] Sriraman, R., Nedunchezhiyan, A.: Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses. Kybernetika 58 (2022), 4, 498-521. DOI  | MR 4521853
[46] Sriraman, R., Cao, Y., Samidurai, R.: Global asymptotic stability of stochastic complexvalued neural networks with probabilistic time-varying delays. Math. and Comput. Simul. 171 (2020), 103-118. DOI  | MR 4066164
[47] Ali, M. S., Yogambigai, J., Saravanan, S., Elakkia, S.: Stochastic stability of neutraltype Markovian-jumping BAM neural networks with time varying delays. J. Comput. and Appl. Math. 349 (2019), 142-156. DOI  | MR 3886702
[48] Tan, Y., Tang, S., Chen, X.: Robust stability analysis of impulsive complex-valued neural networks with mixed time delays and parameter uncertainties. Adv. Diff. Eqns 62 (2018). DOI  | MR 3766070
[49] Tian, J., Xie, X.: New asymptotic stability criteria for neural networks with timevarying delay. Phys. Lett. A 374 (2010), 7, 938-943. DOI  | MR 2580319
[50] Wang, Z., Huang, L.: Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173 (2016), 3, 2083-2089. DOI 
[51] Wu, M., Liu, F., Shi, P., He, Y., Yokoyama, R.: Exponential stability analysis for neural networks with time-varying delay. IEEE Trans. Syst. Man Cybernet., Part B: Cybernetics 38 (2008), 4, 1152-1156. DOI  | MR 0697005
[52] Xie, D., Jiang, Y.: Global exponential stability of periodic solution for delayed complexvalued neural networks with impulses. Neurocomputing 207 (2016), 528-538. DOI 
[53] Xu, C. J., Mu, D., Pan, Y., Aouiti, C., Yao, L.: Exploring bifurcation in a fractional-order predator-prey system with mixed delays. J. Appl. Anal. Comput.13 (2023), 3, 1119-1136. DOI  | MR 4593704
[54] Xu, M., Du, B.: Dynamic behaviors for reaction-diffusion neural networks with mixed delays. AIMS Math. 5 (2020), 6, 6841-6855. DOI  | MR 4148983
[55] Yu, J., Zhang, K., Fei, S.: Mean square exponential stability of generalized stochastic neural networks with time-varying delays. Asian J. Control 11 (2009), 6, 633-642. DOI  | MR 2791309
[56] Zhang, W., Li, C.: Global robust stability of complex-valued recurrent neural networks with time-delays and uncertainties. Int. J. Biomath. 7 (2014), 2, 24 pages. DOI  | MR 3189684
[57] Zhang, W., Li, C., Huang, T., Tan, J.: Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Computing Appl. 26 (2015), 1781-1787. DOI 
[58] Zhang, X., Li, X.: Input-to-state stability of non-linear systems with distributeddelayed impulses. IET Control Theory Appl. 11 (2017), 1, 81-89. DOI  | MR 3644361
[59] Zhang, Z., Lin, C., Chen, B.: Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans. Neur. Netw. Learn. Systems 25 (2014), 9, 1704-1708. DOI 
[60] Zhou, B., Song, Q.: Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans. Neur. Netw. Learn. Systems 24 (2013), 1227-1238. DOI 
[61] Zhou, Q., Wan, L., Fu, H., Zhang, Q.: Exponential stability of stochastic Hopfield neural network with mixed multiple delays. AIMS Math. 6 (2021), 4, 4142-4155. DOI  | MR 4220400
[62] Zhou, W., Li, B., Zhang, J. E.: Matrix measure approach for stability and synchronization of complex-valued neural networks with deviating argument. Mathemat. Probl. Engrg. Article ID 8877129; (2020), 16 pages. DOI  | MR 4178860
[63] Zou, K., Li, X., Wang, N., Lou, J., Lu, J.: Stability and stabilization of delayed neural networks with hybrid impulses. Complexity Article ID 8712027; (2020), 9 pages. DOI 
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