Abstract
This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects. New and practical conditions are given to study the existence, uniqueness, and global exponential stability of anti-periodic solutions for the suggested system. We use differential inequality techniques to prove our main results. Finally, we give an illustrative example to demonstrate the effectiveness of our new results.
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References
Alimi AM, Aouiti C, Chérif F, et al., 2018. Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing, 321:274–295. https://doi.org/10.1016/j.neucom.2018.01.061
Aouiti C, 2018. Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neur Comput Appl, 29(9):477–495. https://doi.org/10.1007/s00521-016-2558-3
Aouiti C, Assali EA, 2019. Stability analysis for a class of impulsive bidirectional associative memory (BAM) neural networks with distributed delays and leakage time-varying delays. Neur Process Lett, 50(1):851–885. https://doi.org/10.1007/s11063-018-9937-y
Aouiti C, Dridi F, 2019a. New results on impulsive Cohen—Grossberg neural networks. Neur Process Lett, 49(3):1459–1483. https://doi.org/10.1007/s11063-018-9880-y
Aouiti C, Dridi F, 2019b. Piecewise asymptotically almost automorphic solutions for impulsive non-autonomous high-order Hopfield neural networks with mixed delays. Neur Comput Appl, 31(9):5527–5545. https://doi.org/10.1007/s00521-018-3378-4
Aouiti C, Miaadi F, 2018. Finite-time stabilization of neutral Hopfield neural networks with mixed delays. Neur Process Lett, 48(3):1645–1669. https://doi.org/10.1007/s11063-018-9791-y
Aouiti C, Miaadi F, 2019. Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays. Neur Comput Appl, 31(8):4113–4122. https://doi.org/10.1007/s00521-017-3314-z
Aouiti C, Coirault P, Miaadi F, et al., 2017. Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing, 260:378–392. https://doi.org/10.1016/j.neucom.2017.04.048
Aouiti C, Abed Assali E, Cao JD, et al., 2018. Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays. Int J Syst Sci, 49(10):2202–2214. https://doi.org/10.1080/00207721.2018.1496297
Balasubramaniam P, Kalpana M, Rakkiyappan R, 2011. Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math Comput Model, 53(5–6):839–853. https://doi.org/10.1016/j.mcm.2010.10.021
Batchelor M, Baxter R, O’Rourke M, et al., 1995. Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions. J Phys A, 28(10):2759–2770. https://doi.org/10.1088/0305-4470/28/10/009
He X, Li CD, Shu Y, 2012. Bogdanov-Takens bifurcation in a single inertial neuron model with delay. Neurocomputing, 89:193–201. https://doi.org/10.1016/j.neucom.2012.02.019
Ke YQ, Miao CF, 2011. Stability analysis of BAM neural networks with inertial term and time delay. WSEAS Trans Syst, 10(12):425–438.
Ke YQ, Miao CF, 2013a. Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays. Neurocomputing, 117:196–205. https://doi.org/10.1016/j.neucom.2013.01.026
Ke YQ, Miao CF, 2013b. Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neur Comput Appl, 23(3–4):1089–1099. https://doi.org/10.1007/s00521-012-1037-8
Ke YQ, Miao CF, 2013c. Exponential stability of periodic solutions in inertial neural networks with unbounded delay. Int J Math Comput Phys Electr Comput Eng, 7(3):477–486.
Ke YQ, Miao CF, 2017. Anti-periodic solutions of inertial neural networks with time delays. Neur Process Lett, 45(2):523–538. https://doi.org/10.1007/s11063-016-9540-z
Kosko B, 1988. Bidirectional associative memories. IEEE Trans Syst Man Cybern, 18(1):49–60. https://doi.org/10.1109/21.87054
Li HF, Jiang HJ, Hu C, 2016. Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays. Neur Netw, 75:97–109. https://doi.org/10.1016/j.neunet.2015.12.006
Li XD, Song SJ, 2017. Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans Autom Contr, 62(1):406–411. https://doi.org/10.1109/TAC.2016.2530041
Li XD, Wu JH, 2016. Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica, 64:63–69. https://doi.org/10.1016/j.automatica.2015.10.002
Li XD, Ho DWC, Cao JD, 2019. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 99:361–368. https://doi.org/10.1016/j.automatica.2018.10.024
Li YK, 2008. Positive periodic solutions of nonlinear differential systems with impulses. Nonl Anal Theory Meth Appl, 68(8):2389–2405. https://doi.org/10.1016/j.na.2007.01.066
Li YK, Xiang JL, 2019. Existence and global exponential stability of anti-periodic solution for Clifford-valued inertial Cohen-Grossberg neural networks with delays. Neurocomputing, 332:259–269. https://doi.org/10.1016/j.neucom.2018.12.064
Li YK, Yang L, Wu WQ, 2015. Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales. Neurocomputing, 149:536–545. https://doi.org/10.1016/j.neucom.2014.08.020
Liao HY, Zhang ZQ, Ren L, et al., 2017. Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques. Chaos Sol Fract, 104:785–797. https://doi.org/10.1016/j.chaos.2017.09.035
Liu B, Teo KL, Liu XZ, 2008. Robust exponential stabilization for large-scale uncertain impulsive systems with coupling time-delays. Nonl Anal Theory Meth Appl, 68(5):1169–1183. https://doi.org/10.1016/j.na.2006.12.025
Liu BW, 2007. Almost periodic solutions for Hopfield neural networks with continuously distributed delays. Math Comput Simul, 73(5):327–335. https://doi.org/10.1016/j.matcom.2006.05.027
Long ZW, 2016. New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing, 171:503–509. https://doi.org/10.1016/j.neucom.2015.06.070
M’Hamdi MS, Aouiti C, Touati A, et al., 2016. Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci, 36(6):1662–1682. https://doi.org/10.1016/S0252-9602(16)30098-4
Okochi H, 1990. On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators. J Funct Anal, 91(2):246–258. https://doi.org/10.1016/0022-1236(90)90143-9
Qi JT, Li CD, Huang TW, 2015. Stability of inertial BAM neural network with time-varying delay via impulsive control. Neurocomputing, 161:162–167. https://doi.org/10.1016/j.neucom.2015.02.052
Stamova I, Stamov T, Li XD, 2014. Global exponential stability of a class of impulsive cellular neural networks with supremums. Int J Adapt Contr Signal Process, 28(11):1227–1239. https://doi.org/10.1002/acs.2440
Tu ZW, Cao JD, Hayat T, 2016. Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays. Neurocomputing, 171:524–531. https://doi.org/10.1016/j.neucom.2015.06.078
Wheeler DW, Schieve WC, 1997. Stability and chaos in an inertial two-neuron system. Phys D, 105(4):267–284. https://doi.org/10.1016/S0167-2789(97)00008-0
Xu CJ, Li PL, 2016. Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms. J Nonl Sci Appl, 9(3):1285–1305. https://doi.org/10.22436/jnsa.009.03.52
Xu CJ, Zhang QM, 2015. Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay. Neurocomputing, 153:108–116. https://doi.org/10.1016/j.neucom.2014.11.047
Zhang ZQ, Quan ZY, 2015. Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing, 151:1316–1326. https://doi.org/10.1016/j.neucom.2014.10.072
Zhou JW, Li YK, 2009. Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects. Nonl Anal Theory Meth Appl, 71(7–8):2856–2865. https://doi.org/10.1016/j.na.2009.01.140
Zhou QY, Shao JY, 2018. Weighted pseudo-anti-periodic SICNNs with mixed delays. Neur Comput Appl, 29(10):865–872. https://doi.org/10.1007/s00521-016-2582-3
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Yang CAO processed the conceptualization. Chaouki AOUITI and Mahjouba Ben REZEG conducted the analysis and validation, and drafted the manuscript. Yang CAO polished the paper.
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Chaouki AOUITI, Mahjouba Ben REZEG, and Yang CAO declare that they have no conflict of interest.
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Aouiti, C., Rezeg, M.B. & Cao, Y. New results on impulsive type inertial bidirectional associative memory neural networks. Front Inform Technol Electron Eng 21, 324–339 (2020). https://doi.org/10.1631/FITEE.1900181
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DOI: https://doi.org/10.1631/FITEE.1900181
Key words
- Inertial neural networks
- Anti-periodic solutions
- Global exponential stability
- Impulsive effect
- Time-varying delay
- Bidirectional associative memory