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Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks

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  • Oliveira, José J.

Abstract

For a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay, we give sufficient conditions for its global asymptotic stability. The main stability criterion depends on the size of the delay on the linear part and the dominance of the linear terms over the nonlinear terms. We apply our main result to answer several open problems left by Berezansky et al. (2014). Using the obtained theoretical stability results, we get sufficient conditions for both the global asymptotic and global exponential stability of a bidirectional associative memory neural network model with delays which generalizes models recently studied. Finally, a numerical example is given to illustrate the novelty of our results.

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  • Oliveira, José J., 2022. "Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008554
    DOI: 10.1016/j.chaos.2022.112676
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    References listed on IDEAS

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    1. Huang, Chengdai & Meng, Yijie & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "New bifurcation results for fractional BAM neural network with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 31-44.
    2. Aouiti, Chaouki & Ben Gharbia, Imen & Cao, Jinde & Salah M’hamdi, Mohammed & Alsaedi, Ahmed, 2018. "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, Elsevier, vol. 107(C), pages 111-127.
    3. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Berezansky, Leonid & Diblík, Josef & Svoboda, Zdeněk & Šmarda, Zdeněk, 2018. "Exponential stability of linear delayed differential systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 474-484.
    6. Maharajan, C. & Raja, R. & Cao, Jinde & Rajchakit, G. & Tu, Zhengwen & Alsaedi, Ahmed, 2018. "LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 33-55.
    7. Thoiyab, N. Mohamed & Muruganantham, P. & Zhu, Quanxin & Gunasekaran, Nallappan, 2021. "Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    1. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Li, Xuemei & Liu, Xinge & Wang, Fengxian, 2023. "Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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