\(p\)th moment exponential stability of memristor Cohen-Grossberg BAM neural networks with time-varying delays and reaction-diffusion. (English) Zbl 07839817
Summary: In this paper, stability for a class of stochastic memristor Cohen-Grossberg BAM neural networks with time-varying delays and reaction-diffusion are considered. A set of novel sufficient conditions on \(p\)th moment exponential stability of the equilibrium point are investigated for the considered system. We constructed Lyapunov functional and utilized stochastic stability theory and Itô’s differential formula. Finally, two examples are provided to illustrate the effectiveness of the derived main results.
MSC:
| 34Kxx | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 92Bxx | Mathematical biology in general |
| 93Cxx | Model systems in control theory |
References:
| [1] | Chua, L. O.; Yang, L., Cellular neural networks: Applications, IEEE Transactions on Circuits and Systems, 35, 1273-1290, (1988) |
| [2] | Hopfield, J., Neural networks and physical systems with emergent collective computational abilities, Proceedings of National Academy of Science, 79, 2554-2558, (1982) · Zbl 1369.92007 |
| [3] | Lv, Z.-S.; Zhu, C.-P.; Nie, P.; Zhao, J.; Yang, H.-J.; Wang, Y.-J.; Hu, C.-K., Exponential distance distribution of connected neurons in simulations of two-dimensional in vitro neural network development, Front. Phys., 12, Article 128902 pp., (2017) |
| [4] | Zeng, H.-L.; Zhu, C.-P.; Wang, S.-X.; Guo, Y.-D.; Gu, Z.-M.; Hu, C.-K., Scaling behaviors and self-organized criticality of two-dimensional small-world neural networks, Physica A, 540, Article 123191 pp., (2020) |
| [5] | Syed Ali, M.; Saravanan, S.; Palanisamy, L., Stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time-varying delays, Chinese J. Phys., 57, 314-328, (2019) · Zbl 1539.93190 |
| [6] | Vadivel, R.; Syed Ali, M.; Alzahrani, F., Robust h-infinity synchronization of Markov jump stochastic uncertain neural networks with decentralized event-triggered mechanism, Chinese J. Phys., 60, 68-87, (2019) · Zbl 07823572 |
| [7] | Cao, J.; Liang, J., Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays, J. Math. Anal. Appl., 296, 665-685, (2004) · Zbl 1044.92001 |
| [8] | Syed Ali, M.; Balasubramaniam, P., Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays chaos, journal=solitons and fractals, 42, 4, 2191-2199, (2009) · Zbl 1198.93192 |
| [9] | Gopalsamy, K.; He, X., Delay-independent stability in bi-directional associative memory with axonal signal transmission delays, IEEE Trans. Neural Netw., 5, 998-1002, (1994) |
| [10] | Huang, G.; Cao, J., Multistability in bidirectional associative memory neural networks, Phys. Lett. A, 372, 2842-2854, (2008) · Zbl 1220.92002 |
| [11] | Syed Ali, M.; Narayanan, G.; Sevgen, S.; Shekher, V.; Arik, S., Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects, Commun. Nonlinear Sci. Numer. Simul., 78, (2019) · Zbl 1461.93420 |
| [12] | Park, J.; Park, C.; Kwon, O.; Lee, S., A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199, 716-722, (2008) · Zbl 1149.34345 |
| [13] | Cohen, M. A.; Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst. Man Cybern., 13, 815-821, (1983) · Zbl 0553.92009 |
| [14] | Kosko, B., Adaptive bidirectional associative memories, Appl. Opt., 26, 4947-4960, (1987) |
| [15] | Kosko, B., Bi-directional associative memories, IEEE Trans. Syst. Man Cybern., 18, 49-60, (1988) |
| [16] | Kosko, B., Neural Networks and Fuzzy Systems - a Dynamical System Approach Machine Intelligence, (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0755.94024 |
| [17] | Xiong, W.; Cao, J., Global exponential stability of discrete-time Cohen-Grossberg neural networks, Neurocomputing, 64, 433-446, (2005) |
| [18] | 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, 1314-1325, (2010) |
| [19] | Syed Ali, M.; Balasubramaniam, P., Exponential stability of uncertain stochastic fuzzy BAM neural networks with time-varying delays, Neurocomputing, 72, 1347-1354, (2009) · Zbl 1198.93192 |
| [20] | Syed Ali, M.; Balasubramaniam, P., Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays, Chaos Solitons Fractals, 42, 2191-2199, (2009) · Zbl 1198.93192 |
| [21] | Chen, A.; Cao, J.; Huang, L., Exponential stability of BAM neural networks with transmission delays, Neurocomputing, 57, 435-464, (2004) |
| [22] | Song, Q.; Cao, J., Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms, Chaos Solitons Fractals, 23, 421-430, (2005) · Zbl 1068.94534 |
| [23] | Zhu, Q.; Huang, C.; Yang, X., Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays, Nonlinear Anal. Hybrid syst, 5, 52-57, (2011) · Zbl 1216.34081 |
| [24] | Zhu, E.; Zhang, H.; Wang, Y.; Zou, J.; Yu, Z.; Hou, Z., \(p\) th moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays, Neural Process Letters, 26, 191-200, (2007) · Zbl 1445.92012 |
| [25] | Huang, C.; Cao, J., On \(p\) th moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays, Neurocomputing, 73, 986-990, (2010) |
| [26] | Xu, C.; Li, P., \(pTh\) moment exponential stability of stochastic fuzzy Cohen-Grossberg neural networks with discrete and distributed delays, Nonlinear Anal. Model. Control, 22, 531-544, (2017) · Zbl 1416.93197 |
| [27] | Wang, F.; Chen, Y.; Liu, M., \(pTh\) moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays, Neural Netw., 98, 192-202, (2018) · Zbl 1442.34132 |
| [28] | Syed Ali, M.; Saravanan, S.; Esther Rani, M.; Elakkia, S.; Cao, J., Asymptotic stability of Cohen-Grossberg BAM neutral type neural networks with distributed time varying delays, Neural Process. Lett., 46, 991-1007, (2017) |
| [29] | Syed Ali, M.; Balasubramaniam, P.; Rihan, F. A.; Lakshmanan, S., Stability criteria for stochastic Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with mixed time-varying delays, Complexity, 21, 143-154, (2016) |
| [30] | Cao, J.; Song, Q., Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays, Nonlinearity, 19, 1601, (2006) · Zbl 1118.37038 |
| [31] | Li, X., Exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control, Neurocomputing, 73, 525-530, (2009) |
| [32] | Chua, L., Memristor-the missing circuit element, IEEE Transactions on Circuit Theory CT, 18, 507-519, (1971) |
| [33] | Strukov, D. B.; Snider, G. S.; Stewart, G. R.; Williams, R. S., The missing memristor found, Nature, 453, 80-83, (2008) |
| [34] | Yang, X.; Cao, J.; Qiu, J., \(pTh\) moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control, Neural networks, 65, 80-91, (2015) · Zbl 1398.34121 |
| [35] | Li, R.; Cao, J., Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term, Appl. Math. Comput., 278, 54-69, (2016) · Zbl 1410.93088 |
| [36] | Wei, H.; Chen, C.; Tu, Z.; Li, N., New results on passivity analysis of memristive neural networks with time-varying delays and reaction-diffusion terms, Neurocomputing, 275, 2080-2092, (2018) |
| [37] | Wu, A.; Zeng, Z., Exponential stabilization of memristive neural networks with time delays, IEEE Trans. Neural Netw. Learn. Syst., 23, 1919-1929, (2012) |
| [38] | Zhang, G. D.; Shen, Y.; Yin, Q.; Sun, J. W., Globally exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays, Inform. Sci., 232, 386-396, (2013) · Zbl 1293.34094 |
| [39] | Syed Ali, M.; Saravanakumar, R.; Cao, J., New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays, Neurocomputing, 171, 1533-1547, (2016) |
| [40] | Li, H.; Jiang, H.; C, J., Hu existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural Netw., 75, 97-109, (2016) · Zbl 1417.34164 |
| [41] | Balasubramaniam, P.; Syed Ali, M., Robust stability of uncertain fuzzy cellular neural networks with time-varying delays and reaction diffusion terms, Neurocomputing, 74, 439-446, (2010) |
| [42] | Li, X.; Cao, J., Delay-independent of exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms, Nonlinear Dynam., 50, 363-371, (2007) · Zbl 1176.92004 |
| [43] | Song, Q.; Zhao, Z.; Li, Y., Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms, Phys. Lett. A, 335, 213-225, (2005) · Zbl 1123.68347 |
| [44] | Wang, Y.; Cao, J., Exponential stability of stochastic higher-order BAM neural networks with reaction-diffusion terms and mixed time-varying delays, Neurocomputing, 119, 192-200, (2013) |
| [45] | Wan, L.; Zhou, Q., Global exponential stability of BAM neural networks with time-varying delays and diffusion terms, Phys. Lett. A, 371, 83-89, (2007) · Zbl 1209.93107 |
| [46] | Balasubramaniam, P.; Vidhya, C., Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms, J. Comput. Appl. Math., 234, 3458-3466, (2010) · Zbl 1198.35025 |
| [47] | Chen, A.; Huang, L.; Cao, J., Exponential stability of delayed bidirectional associative memory neural networks with reaction-diffusion terms, International journal of systems science, 38, 421-432, (2007) · Zbl 1130.35348 |
| [48] | Syed Ali, M.; Saravanan, S.; Palanisamy, L., Stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time-varying delays, Chinese J. Phys., 57, 314-328, (2019) · Zbl 1539.93190 |
| [49] | Zhu, Q.; Li, X.; Yang, X., Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distribyted delays, Appl. Math. Comput., 217, 6078-6091, (2011) · Zbl 1210.35308 |
| [50] | Mao, X., Stochastic Differential Equations and their Applications, (1997), Horwood: Horwood Chichester, UK · Zbl 0892.60057 |
| [51] | Syed Ali, M.; Balasubramaniam, P.; Zhu, Q., Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays, Int. J. Mach. Learn. Cybern., 8, 263-273, (2017) |
| [52] | Zhu, Q.; Cao, J., Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays, Neurocomputing, 73, 2671-2680, (2010) |
| [53] | 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 |
| [54] | 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. B, 342, 1489-1510, (2010) · Zbl 1202.93169 |
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