Research article

New convergence on inertial neural networks with time-varying delays and continuously distributed delays

  • Received: 22 May 2020 Accepted: 08 July 2020 Published: 21 July 2020
  • MSC : 34C25, 34K13, 34K25

  • In this paper, a class of inertial neural networks with bounded time-varying delays and unbounded continuously distributed delays are explored by applying non-reduced order method. Based upon differential inequality techniques and Lyapunov function method, a new sufficient condition is presented to ensure all solutions of the addressed model and their derivatives converge to zero vector, which refines some previously known researches. Moreover, a numerical example is provided to illustrate these analytical conclusions.

    Citation: Qian Cao, Xin Long. New convergence on inertial neural networks with time-varying delays and continuously distributed delays[J]. AIMS Mathematics, 2020, 5(6): 5955-5968. doi: 10.3934/math.2020381

    Related Papers:

  • In this paper, a class of inertial neural networks with bounded time-varying delays and unbounded continuously distributed delays are explored by applying non-reduced order method. Based upon differential inequality techniques and Lyapunov function method, a new sufficient condition is presented to ensure all solutions of the addressed model and their derivatives converge to zero vector, which refines some previously known researches. Moreover, a numerical example is provided to illustrate these analytical conclusions.


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    [1] K. Babcock, R. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Phys. D, 23 (1986), 464-469. doi: 10.1016/0167-2789(86)90152-1
    [2] Y. Zhou, X. Wan, C. Huang, et al. Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control, Appl. Math. Comput., 376 (2020), 125157.
    [3] C. Huang, B. Liu, New studies on dynamic analysis of inertial neural networks involving nonreduced order method, Neurocomputing, 325 (2019), 283-287. doi: 10.1016/j.neucom.2018.09.065
    [4] C. Huang, Exponential stability of inertial neural networks involving proportional delays and nonreduced order method, J. Exp. Theor. Artif. Intell., 32 (2020), 133-146. doi: 10.1080/0952813X.2019.1635654
    [5] Z. Cai, J. Huang, L. Huang, Periodic orbit analysis for the delayed Filippov system, Proc. Am. Math. Soc., 146 (2018), 4667-4682. doi: 10.1090/proc/13883
    [6] C. Huang, R. Su, J. Cao, et al. Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators, Math. Comput. Simulation, 171 (2020), 127-135. doi: 10.1016/j.matcom.2019.06.001
    [7] X. Yang, S. Wen, Z. Liu, et al. Dynamic properties of foreign exchange complex network, Mathematics, 7 (2019), 832.
    [8] C. Huang, X. Yang, J. Cao, Stability analysis of Nicholson's blowflies equation with two different delays, Math. Comput. Simulation, 171 (2020), 201-206. doi: 10.1016/j.matcom.2019.09.023
    [9] C. Huang, J. Wang, L. Huang, Asymptotically almost periodicity of delayed Nicholson-type system involving patch structure, Electron. J. Differ. Equ., 2020 (2020), 1-17. doi: 10.1186/s13662-019-2438-0
    [10] H. Zhao, X. Yu, L. Wang, Bifurcation and control in an inertial two-neuron system with time delays, Int. J. Bifurcat. Chaos, 22 (2012), 1250036.
    [11] C. Huang, X. Long, J. Cao, Stability of anti-periodic recurrent neural networks with multiproportional delays, Math. Methods Appl. Sci., 43 (2020), 6093-6102. doi: 10.1002/mma.6350
    [12] C. Huang, L. Yang, J. Cao, Asymptotic behavior for a class of population dynamics, AIMS Math., 5 (2020), 3378-3390. doi: 10.3934/math.2020218
    [13] Q. Cao, X. Guo, Anti-periodic dynamics on high-order inertial Hopfield neural networks involving time-varying delays, AIMS Math., 5 (2020), 5402-5421. doi: 10.3934/math.2020347
    [14] C. Huang, S.Wen, M. Li, et al. An empirical evaluation of the influential nodes for stock market network: Chinese A-shares case, Finance Res. Lett., (2020), 101517.
    [15] L. Duan, L. Huang, Z. Guo, et al. Periodic attractor for reaction-diffusion high-order hopfield neural networks with time-varying delays, Comput. Math. Appl., 73 (2017), 233-245. doi: 10.1016/j.camwa.2016.11.010
    [16] S. Wen, Y. Tan, M. Li, et al. Analysis of global remittance based on complex networks, Front. Phys., 8 (2020), 1-9. doi: 10.3389/fphy.2020.00001
    [17] T. Chen, L. Huang, P. Yu, et al. Bifurcation of limit cycles at infinity in piecewise polynomial systems, Nonlinear Anal. Real World Appl., 41 (2018), 82-106. doi: 10.1016/j.nonrwa.2017.10.003
    [18] J. Wang, X. Chen, L. Huang, The number and stability of limit cycles for planar piecewise linear systems of node-saddle type, J. Math. Anal. Appl., 469 (2019), 405-427. doi: 10.1016/j.jmaa.2018.09.024
    [19] Z. Ye, C. Hu, L. He, et al. The dynamic time-frequency relationship between international oil prices and investor sentiment in China: A wavelet coherence analysis, Energy J., 41 (2020). DOI: 10.5547/01956574.41.5.fwen.
    [20] X. Li, X. Li, C. Hu, Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method, Neural Networks, 96 (2017), 91-100. doi: 10.1016/j.neunet.2017.09.009
    [21] C. Huang, H. Kuang, X. Chen, et al. An LMI approach for dynamics of switched cellular neural networks with mixed delays, Abstr. Appl. Anal., 2013 (2013), 1-8.
    [22] Y. Ke, C. Miao, Anti-periodic solutions of inertial neural networks with time delays, Neural Process. Lett., 45 (2017), 523-538. doi: 10.1007/s11063-016-9540-z
    [23] C. Xu, Q. Zhang, Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay, Neurocomputing, 153 (2015), 108-116. doi: 10.1016/j.neucom.2014.11.047
    [24] L. Wang, M. Ge, J. Hu, et al. Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays, Nonlinear Dyn., 95 (2019), 943-955. doi: 10.1007/s11071-018-4606-2
    [25] L. Wang, H. He, Z. Zeng, Global synchronization of fuzzy memristive neural networks with discrete and distributed delays, IEEE Trans. Fuzzy Syst., (2019), 1-12. DOI: 10.1109/TFUZZ.2019.2930032.
    [26] L. Wang, Z. Zeng, M. Ge, A disturbance rejection framework for finite-time and fixed-time stabilization of delayed memristive neural networks, IEEE Transactions on Systems, Man, and Cybernetics, (2019), 1-11. DOI: 10.1109/TSMC.2018.2888867.
    [27] J. Zhao, J. Liu, L. Fang, Anti-periodic boundary value problems of second-order functional differential equations, Bull. Malays. Math. Sci. Soc., 37 (2014), 311-320.
    [28] C. Aouiti, I. B. Gharbia, Dynamics behavior for second-order neutral Clifford differential equations: Inertial neural networks with mixed delays, Comput. Appl. Math., 39 (2020), 1-31. doi: 10.1007/s40314-019-0964-8
    [29] C. Aouiti, E. A. Assali, Effect of fuzziness on the stability of inertial neural networks with mixed delay via non-reduced-order method, Int. J. Comput. Math. Comput. Syst. Th., 4 (2019), 151-170, 30. C. Huang, C. Peng, X. Chen, et al. Dynamics analysis of a class of delayed economic model, Abstr.
    [30] Appl. Anal., 2013 (2013), 1-12.
    [31] L. Wang, Z. Zeng, M. Ge, et al. Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays, Neural Networks, 105 (2018), 65-74. doi: 10.1016/j.neunet.2018.04.014
    [32] C. Huang, B. Liu, X. Tian, Global convergence on asymptotically almost periodic SICNNs with nonlinear decay functions, Neural Process. Lett., 49 (2019), 625-641. doi: 10.1007/s11063-018-9835-3
    [33] K. Zhu, Y. Xie, F. Zhou, Pullback attractors for a damped semilinear wave equation with delays, Acta Math. Sin. (Engl. Ser.), 34 (2018), 1131-1150. doi: 10.1007/s10114-018-7420-3
    [34] J. Wang, C. Huang, L. Huang, Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type, Nonlinear Anal. Hybrid Syst., 33 (2019), 162-178. doi: 10.1016/j.nahs.2019.03.004
    [35] J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equ., 2020 (2020), 1-12. doi: 10.1186/s13662-019-2438-0
    [36] Y. Xu, Convergence on non-autonomous inertial neural networks with unbounded distributed delays, J. Exp. Theor. Artif. Intell., 32 (2020), 503-513. doi: 10.1080/0952813X.2019.1652941
    [37] C. Huang, H. Yang, J. Cao, Weighted pseudo almost periodicity of multi-proportional delayed shunting inhibitory cellular neural networks with D operator, Discrete Contin. Dyn. Syst. Ser. S, (2018), 1-14. DOI:10.3934/dcdss.2020372.
    [38] L. Yao, Q. Cao, Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays, J. Inequal. Appl., (2020), Available from: https://doi.org/10.1186/s13660-020-02444-3.
    [39] J. Li, J. Ying, D. Xie, On the analysis and application of an ion size-modified Poisson-Boltzmann equation, Nonlinear Anal. Real World Appl., 47 (2019), 188-203. doi: 10.1016/j.nonrwa.2018.10.011
    [40] Y. Hino, S. Murakami, T. Naito, Functional differential equations with infinite delay, In Lecture in math-ematics Berlin: Springer, 1991.
    [41] Q. Cao, G. Wang, C. Qian, New results on global exponential stability for a periodic Nicholson's blowflies model involving time-varying delays, Adv. Differ. Equ., 2020 (2020), 43.
    [42] H. Hu, T. Yi, X. Zou, On spatial-temporal dynamics of Fisher-KPP equation with a shifting environment, Proc. Am. Math. Soc., 148 (2020), 213-221.
    [43] X. Long, S. Gong, New results on stability of Nicholson's blowflies equation with multiple pairs of time-varying delays, Appl. Math. Lett., 100 (2020), 106027.
    [44] C. Huang, H. Zhang, L. Huang, Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term, Commun. Pure Appl. Anal., 18 (2019), 3337-3349. doi: 10.3934/cpaa.2019150
    [45] C. Huang, H. Zhang, J. Cao, et al. Stability and Hopf bifurcation of a delayed prey-predator model with disease in the predator, Int. J. Bifurcation Chaos, 29 (2019), 1950091.
    [46] H. Zhang, Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics, Discrete Contin. Dyn. Syst., 39 (2019), 6669-6682. doi: 10.3934/dcds.2019290
    [47] X. Zhang, H. Hu, Convergence in a system of critical neutral functional differential equations, Appl. Math. Lett., 107 (2020), 106385.
    [48] C. Qian, New periodic stability for a class of Nicholson's blowflies models with multiple different delays, Int. J. Control, (2020), 1-13. DOI: 10.1080/00207179.2020.1766118.
    [49] C. Huang, X. Long, L. Huang, et al. Stability of almost periodic Nicholson's blowflies model involving patch structure and mortality terms, Can. Math. Bull., 63 (2020), 405-422. doi: 10.4153/S0008439519000511
    [50] Y. Xu, Q. Cao, X. Guo, Stability on a patch structure Nicholson's blowflies system involving distinctive delays, Appl. Math. Lett., 105 (2020), 106340,
    [51] H. Hu, X. Yuan, L. Huang, et al. Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks, Math. Biosci. Eng., 16 (2019), 5729-5749. doi: 10.3934/mbe.2019286
    [52] Y. Tan, Dynamics analysis of Mackey-Glass model with two variable delays, Math. Biosci. Eng., 17 (2020), 4513-4526. doi: 10.3934/mbe.2020249
    [53] L. Li, Q. Jin, B. Yao, Regularity of fuzzy convergence spaces, Open Math., 16 (2018), 1455-1465. doi: 10.1515/math-2018-0118
    [54] C. Huang, L. Liu, Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation, Quaest. Math., 40 (2017), 295-312. doi: 10.2989/16073606.2017.1287136
    [55] C. Huang, J. Cao, F. Wen, et al. Stability analysis of SIR model with distributed delay on complex networks, PLoS One, 11 (2016), e0158813.
    [56] X. Li, Y. Liu, J. Wu, Flocking and pattern motion in a modified cucker-smale model, Bull. Korean Math. Soc., 53 (2016), 1327-1339. doi: 10.4134/BKMS.b150629
    [57] Y. Xie, Q. Li, K. Zhu, Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity, Nonlinear Anal. Real World Appl., 31 (2016), 23-37. doi: 10.1016/j.nonrwa.2016.01.004
    [58] F. Wang, P. Wang, Z. Yao, Approximate controllability of fractional partial differential equation, Adv. Differ. Equ., 2015 (2015), 1-10. doi: 10.1186/s13662-014-0331-4
    [59] Y. Liu, J. Wu, Multiple solutions of ordinary differential systems with min-max terms and applications to the fuzzy differential equations, Adv. Differ. Equ., 2015 (2015), 1-13. doi: 10.1186/s13662-014-0331-4
    [60] L. Yan, J. Liu, Z. Luo, Existence and multiplicity of solutions for second-order impulsive differential equations on the half-line, Adv. Differ. Equ., 2013 (2013), 1-12, doi: 10.1186/1687-1847-2013-1
    [61] Y. Liu, J. Wu, Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems, Math. Methods Appl. Sci., 37 (2014), 508-517. doi: 10.1002/mma.2809
    [62] X. Li, Z. Liu, J. Li, Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces, Acta Math. Sci., 39 (2019), 229-242. doi: 10.1007/s10473-019-0118-5
    [63] C. Qian, Y. Hu, Novel stability criteria on nonlinear density-dependent mortality Nicholson's blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl., 2020 (2020), 1-18. doi: 10.1186/s13660-019-2265-6
    [64] S. Zhou, Y. Jiang, Finite volume methods for N-dimensional time fractional Fokker-Planck equations, Bull. Malays. Math. Sci. Soc., 42 (2019), 3167-3186. doi: 10.1007/s40840-018-0652-7
    [65] Y. Tan, C. Huang, B. Sun, et al. Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition, J. Math. Anal. Appl., 458 (2018), 1115-1130. doi: 10.1016/j.jmaa.2017.09.045
    [66] F. Liu, L. Feng, A. Vo, et al. Unstructured-mesh Galerkin finite element method for the twodimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains, Comput. Math. Appl., 78 (2019), 1637-1650. doi: 10.1016/j.camwa.2019.01.007
    [67] Q. Jin, L. Li, G. Lang, p-regularity and p-regular modification in T-convergence spaces, Mathematics, 7 (2019), 370.
    [68] L. Huang, Endomorphisms and cores of quadratic forms graphs in odd characteristic, Finite Fields Appl, 55 (2019), 284-304. doi: 10.1016/j.ffa.2018.10.006
    [69] L. Huang, B. Lv, K. Wang, Erdos-Ko-Rado theorem, Grassmann graphs and p(s)-Kneser graphs for vector spaces over a residue class ring, J. Combin. Theory Ser. A, 164 (2019), 125-158.
    [70] Y. Li, M. Vuorinen, Q. Zhou, Characterizations of John spaces, Monatsh. Math., 188 (2019), 547-559. doi: 10.1007/s00605-018-1231-6
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