Stability analysis of stochastic BAM neural networks with reaction-diffusion, multi-proportional and distributed delays. (English) Zbl 07570014
Summary: This paper is devoted to investigating of the stability for stochastic reaction-diffusion BAM neural networks with mixed delays. By applying some new analysis methods, several novel exponential stability criteria are obtained. Our results extend some existing results on stochastic BAM neural networks including with/without reaction-diffusion, time-varying (TV) and multi-proportional delays. In particular, we consider the effect of TV, distributed and multi-proportional delays. An example is provided to show the effectiveness of the obtained results.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
BAM neural network; multi-proportional delay; distributed delay; Lyapunov-Krasovskii functional; reaction-diffusionReferences:
| [1] | Kosko, B., Adaptive bidirectional associative memories, Appl. Opt., 26, 23, 4947-4960 (1987) |
| [2] | Syed Ali, M.; Yogambigai, J.; Saravanan, S.; Elakkia, S., Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays, J. Comput. Appl. Math., 349, 142-156 (2019) · Zbl 1406.34095 |
| [3] | Wang, F.; Liu, M., Glopal exponential stability of high-order bidirectional associative memory BAMNNs with time-delays in leakage terms, Neurocomputing, 177, 515-528 (2016) |
| [4] | Jia, R., Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays, Fuzzy Sets and Systems, 319, 70-80 (2017) · Zbl 1385.34052 |
| [5] | Zhou, L.; Zhang, Y., Global exponential stability of cellular neural networks with multi-proportional delays, Int. J. Biomath., 8, 6, 1-17 (2015) · Zbl 1332.34117 |
| [6] | Zhou, L.; Zhang, Y., Global exponential periodicity and stability of recurrent neural networks with multi-proportional delays, ISA Trans., 60, 89-95 (2016) |
| [7] | Zhu, Q.; Cao, J., Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Netw., 21, 8, 1314-1325 (2010) |
| [8] | Muralisankar, S.; Manivannan, A.; Balasubramaniam, P., Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks, ISA Trans., 58, 11-19 (2015) |
| [9] | Zhu, Q.; Cao, J., Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays, IEEE Trans. Syst. Man Cybern., 41, 2, 341-353 (2011) |
| [10] | Guo, Y., Mean square exponential stability of stochastic delay cellular neural networks, Electron. J. Qual. Theory Differ. Equ., 34, 1-10 (2013) · Zbl 1340.34306 |
| [11] | Li, D.; Cheng, P.; Hua, M.; Yao, F., Robust exponential stability of uncertain impulsive stochastic neural networks with delayed impulses, J. Franklin Inst., 355, 17, 8597-8618 (2018) · Zbl 1402.93196 |
| [12] | Rathinasamy, A.; Narayanasamy, J., Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks, Appl. Math. Comput., 348, 126-152 (2019) · Zbl 1429.65021 |
| [13] | Zhu, Q.; Cao, J., Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays, Neurocomputing, 73, 13-15, 2671-2680 (2010) |
| [14] | Guo, Y., Globally robust stability analysis for stochastic Cohen-Grossberg neural networks with impulse and time-varying delays, Ukrainian Math. J., 69, 8, 1049-1060 (2017) · Zbl 1426.93352 |
| [15] | Zhu, Q.; Yang, X.; Wang, H., Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances, J. Franklin Inst., 347, 2, 1489-1510 (2010) · Zbl 1202.93169 |
| [16] | Jiao, S.; Shen, H.; Wei, Y.; Huang, X.; Wang, Z., Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays, Appl. Math. Comput., 336, 338-350 (2018) · Zbl 1427.93262 |
| [17] | Zhu, Q.; Li, X.; Yang, X., Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays, Appl. Math. Comput., 217, 13, 6078-6091 (2011) · Zbl 1210.35308 |
| [18] | Balasubramaniam, P.; Vidhya, C., Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms, J. Comput. Appl. Math., 234, 12, 3458-3466 (2010) · Zbl 1198.35025 |
| [19] | Sheng, Y.; Zeng, Z., Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays, Neural Netw., 103, 83-93 (2018) · Zbl 1441.93328 |
| [20] | Zhu, Q.; Cao, J., Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Trans. Neural Netw. Learn. Syst., 23, 3, 467-479 (2012) |
| [21] | Zhu, Q.; Rakkiyappan, R.; Chandrasekar, A., Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control, Neurocomputing, 136, 136-151 (2014) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
