AIMS Mathematics, 2020, 5(6): 5955-5968. doi: 10.3934/math.2020381

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

1 College of Mathematics and Physics, Hunan University of Arts and Science, Changde, 415000, Hunan, P. R. China
2 School of Mathematics and Statistics, Changsha University of Science and Technology; Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, Hunan, P. R. China

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.
  Figure/Table
  Supplementary
  Article Metrics

References

1. K. Babcock, R. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Phys. D, 23 (1986), 464-469.    

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.    

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.    

5. Z. Cai, J. Huang, L. Huang, Periodic orbit analysis for the delayed Filippov system, Proc. Am. Math. Soc., 146 (2018), 4667-4682.    

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.    

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.    

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.    

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.    

12. C. Huang, L. Yang, J. Cao, Asymptotic behavior for a class of population dynamics, AIMS Math., 5 (2020), 3378-3390.    

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.    

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.    

16. S. Wen, Y. Tan, M. Li, et al. Analysis of global remittance based on complex networks, Front. Phys., 8 (2020), 1-9.    

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.    

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.    

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.    

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.    

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.    

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.    

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.    

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.

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.    

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.    

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.    

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.    

35. J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equ., 2020 (2020), 1-12.    

36. Y. Xu, Convergence on non-autonomous inertial neural networks with unbounded distributed delays, J. Exp. Theor. Artif. Intell., 32 (2020), 503-513.    

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.    

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.    

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.    

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.    

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.    

52. Y. Tan, Dynamics analysis of Mackey-Glass model with two variable delays, Math. Biosci. Eng., 17 (2020), 4513-4526.    

53. L. Li, Q. Jin, B. Yao, Regularity of fuzzy convergence spaces, Open Math., 16 (2018), 1455-1465.    

54. C. Huang, L. Liu, Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation, Quaest. Math., 40 (2017), 295-312.    

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.    

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.    

58. F. Wang, P. Wang, Z. Yao, Approximate controllability of fractional partial differential equation, Adv. Differ. Equ., 2015 (2015), 1-10.    

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.    

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,    

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.    

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.    

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.    

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.    

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.    

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.    

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.    

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.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved