×
Wang, Yangling; Cao, Jinde; Huang, Chengdai

Exploration of bifurcation for a fractional-order BAM neural network with \(n+2\) neurons and mixed time delays. (English) Zbl 1505.37103

Chaos Solitons Fractals 159, Article ID 112117, 11 p. (2022).

Cited in 7 Documents

MSC:

37N25 Dynamical systems in biology
92C20 Neural biology
92B20 Neural networks for/in biological studies, artificial life and related topics
26A33 Fractional derivatives and integrals

Keywords:

Hopf bifurcation; fractional-order BAM neural network; neurons; leakage delay; nonuniform communication delays
Cite Review PDF
Full Text: DOI

References:

[1] Kosko, B., Adaptive bi-directional associative memories, Appl Opt, 26, 23, 4947-4960 (1987)
[2] Baldi, P.; Atiya, A., How delays affect neural dynamics and learning, IEEE Trans Neural Netw, 5, 4, 610-621 (1994)
[3] Cao, J. D.; Liang, J. L.; James, J., Exponential stability of high-order bidirectional associative memory neural networks with time delays, Phys D, 199, 3-4, 425-436 (2004) · Zbl 1071.93048
[4] Arik, S., Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays, IEEE Trans Neural Netw, 16, 3, 580-586 (2005)
[5] Zhou, F. Y.; Ma, C. R., Global exponential stability of high-order BAM neural networks with reaction-diffusion terms, Int J Bifurcation Chaos, 20, 10, 3209-3223 (2010) · Zbl 1204.35044
[6] Zhu, Q. X.; Cao, J. D., 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)
[7] Wang, F.; Liu, M. C., Global exponential stability of high-order bidirectional associative memory (BAM) neural networks with time delays in leakage terms, Neurocomputing, 177, C, 515-528 (2016)
[8] Berezansky, L.; Braverman, E.; Idels, L., New global exponential stability criteria for nonlinear delay differential systems with applications to BAM neural networks, Appl Math Comput, 243, 15, 899-910 (2014) · Zbl 1335.92007
[9] Wang, T. Y.; Zhu, Q. X., Stability analysis of stochastic BAM neural networks with reaction-diffusion, multi-proportional and distributed delays, Phys A, 533, Article 121935 pp. (2019) · Zbl 07570014
[10] Chen, A. P.; Chen, F. L., Periodic solution to BAM neural network with delays on time scales, Neurocomputing, 73, 1-3, 274-282 (2009)
[11] Zhang, Z. Q.; Liu, K. Y., Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales, Neural Netw, 24, 5, 427-439 (2011) · Zbl 1222.34108
[12] Aouiti, C.; Gharbia, I. B.; Cao, J. D.; M’hamdi MS, Alsaedi A., Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms, Chaos Solitons Fractals, 107, 111-127 (2018) · Zbl 1380.92006
[13] Song, Y. L.; Han, M. A.; Wei, J. J., Stability and hopf bifurcation on a simplified BAM network model with delays, Phys D, 200, 3-4, 185-204 (2005) · Zbl 1062.34079
[14] Yu, W. W.; Cao, J. D., Stability and hopf bifurcation analysis on a four-neuron BAM neural network with time delays, Phys Lett A, 351, 1-2, 64-78 (2006) · Zbl 1234.34047
[15] Cao, J. D.; Xiao, M., Stability and hopf bifurcation in a simplified BAM neural network with two time delays, IEEE Trans Neural Netw, 18, 2, 416-430 (2007)
[16] Javidmanesh, E.; Afsharnezhad, Z.; Effati, S., Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model, Nonlinear Dyn, 72, 1, 149-164 (2013) · Zbl 1268.92009
[17] Malika, S.; Abdujelil, A.; Jiang, H. J., General decay synchronization of delayed BAM neural networks via nonlinear feedback control, Appl Math Comput, 337, 15, 302-314 (2018) · Zbl 1427.93025
[18] Wang, W. P.; Wang, M. Q.; Xiong, L.; Li, L. X.; Zhao, W. B.; Liu, L. L.; Ping, Y., Passivity of memristive BAM neural networks with leakage and additive time-varying delays, Mod Phys Lett B, 32, 4, Article 1850041 pp. (2018)
[19] Xu, C. J., Local and global hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays, Math Comput Simul, 149, 69-90 (2018) · Zbl 1540.92032
[20] Yang, Y.; Ye, J., Stability and bifurcation in a simplified five-neuron BAM neural network with delays, Chaos Solitons Fractals, 42, 2357-2363 (2009) · Zbl 1198.34170
[21] Javidmanesh, E.; Dadi, Z.; Afsharnezhad, Z.; Effati, S., Global stability analysis and existence of periodic solutions in an eight-neuron BAM neural network model with delays, J Intell Fuzzy Syst, 27, 1, 391-406 (2014) · Zbl 1305.92017
[22] Kosmatopoulos, E. B.; Christodoulou, M. A., Structural properties of gradient recurrent high-order neural networks, IEEE Trans Circuits Syst II, 42, 9, 592-603 (1995) · Zbl 0943.68510
[23] Kosmatopoulos, E. B.; Polycarpou, M. M.; Christodoulou, M. A.; Ioannou, P. A., High-order neural network structures for identification of dynamical systems, IEEE Trans Neural Netw, 6, 2, 422-431 (1995)
[24] Xiao, M.; Zheng, W. X.; Cao, J. D., Hopf bifurcation of an -neuron bidirectional associative memory neural network model with delays, IEEE Trans Neural Netw Learn Syst, 24, 1, 118-132 (2013)
[25] Huang, C. D.; Cao, J. D.; Alofi, A.; AI-Mazrooei A, Elaiw A., Dynamics and control in an -neuron BAM network with multiple delays, Nonlinear Dyn, 87, 1, 313-336 (2017) · Zbl 1371.34104
[26] Gopalsamy, K., Leakage delays in BAM, J Math Anal Appl, 325, 15, 1117-1132 (2007) · Zbl 1116.34058
[27] Lakshmanan, S.; Park, J. H.; Jung, H. Y.; Balasubramaniam, P., Design of state estimator for neural networks with leakage, discrete and distributed delays, Appl Math Comput, 218, 22, 11297-11310 (2012) · Zbl 1277.93078
[28] Li, X. D.; Rakkiyappan, R., Stability results for takagi-sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term, Neural Comput Appl, 22, 1, 203-219 (2013)
[29] Lin, J. Z.; Xu, R.; Li, L. C., Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay, Commun Nonlinear Sci Numer Simul, 85, Article 105241 pp. (2020) · Zbl 1450.35049
[30] Magin, R., Fractional calculus in bioengineering, Crit Rev Biomed Eng, 32, 1, 1-104 (2004)
[31] Kibas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and application of fractional differential equations (2006), Elsevier: Elsevier New York · Zbl 1092.45003
[32] Deng, W. H.; Li, C. P.; Lü, J. H., Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dyn, 48, 409-416 (2007) · Zbl 1185.34115
[33] Wang, Z.; Wang, X. H.; Xia, J. W.; Shen, H.; Meng, B., Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems, Sci China Technol Sci, 63, 9, 1854-1862 (2020)
[34] Meng, B.; Wang, X. H.; Zhang, Z. Y.; Wang, Z., Necessary and sufficient conditions for normalization and sliding mode control of singular fractional-order systems with uncertainties, Sci China Inf Sci, 63, 5, Article 152202 pp. (2020)
[35] Chen, L. P.; Liu, C.; Wu, R. C.; He, Y. G.; Chai, Y., Finite-time stability criteria for a class of fractional-order neural networks with delay, Neural Comput Appl, 27, 3, 549-556 (2016)
[36] Wang, H.; Yu, Y. G.; Wen, G. G., Stability analysis of fractional-order hopfield neural networks with multiple time delays, Neural Netw, 55, 98-109 (2014) · Zbl 1322.93089
[37] Jia, J.; Huang, X.; Li, Y. X.; Cao, J. D., Global stabilization of fractional-order memristor-based neural networks with time delay, IEEE Trans Neural Netw Learn Syst, 31, 3, 997-1009 (2020)
[38] Xu, C. J.; Aouiti, C.; Liu, Z. X., A further study on bifurcation for fractional order BAM neural networks with multiple delays, Neurocomputing, 417, 501-515 (2020)
[39] Xu, C. J.; Liu, Z. X.; Liao, M. X.; Li, P. L.; Xiao, Q. M.; Yuan, S., Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: the case of hopf bifurcation, Math Comput Simul, 182, 471-494 (2021) · Zbl 1524.92014
[40] Huang, C. D.; Meng, Y. J.; Cao, J. D.; Alsaedi, A.; Alsaadi, F. E., New bifurcation results for fractional BAM neural network with leakage delay, Chaos Solitons Fractals, 100, 31-44 (2017) · Zbl 1373.34117
[41] Huang, C. D.; Liu, H.; Chen, Y. F.; Chen, X. P.; Song, F., Dynamics of a fractional-order BAM neural network with leakage delay and communication delay, Fractals, 29, 3, Article 2150073 pp. (2021) · Zbl 1487.34152
[42] Huang, C. D.; Cao, J. D., Impact of leakage delay on bifurcation in high-order fractional BAM neural networks, Neural Netw, 98, 223-235 (2018) · Zbl 1439.93004
[43] Podlubny, I., Fractional differential equations (1999), Academic Press: Academic Press New York · Zbl 0918.34010
[44] Desoer, C., The optimum formula for the gain of a flow graph or a simple derivation of Coates’ formula, Proc IRE, 48, 5, 883-889 (1960)
[45] Bandyopadhyay, B.; Kamal, S., Stabliization and control of fractional order systems: a sliding mode approach, Lect Notes Electr Eng, 317 (2015) · Zbl 1307.93001
[46] Matignon, D., Stability results for fractional differential equations with applications to control processing, Computat Eng Syst Appl, 2, 963-968 (1996)
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.