
AIMS Mathematics, 2020, 5(6): 54025421. doi: 10.3934/math.2020347.
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Antiperiodic dynamics on highorder inertial Hopfield neural networks involving timevarying delays
1 College of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P. R. China
2 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China
Received: , Accepted: , Published:
Keywords: highorder inertial neural networks; antiperiodic solution; global exponential stability; timevarying delay
Citation: Qian Cao, Xiaojin Guo. Antiperiodic dynamics on highorder inertial Hopfield neural networks involving timevarying delays. AIMS Mathematics, 2020, 5(6): 54025421. doi: 10.3934/math.2020347
References:
 1. K. Babcock, R. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Physica D, 23 (1986), 464469.
 2. K. Babcock, R. Westervelt, Dynamics of simple electronic neural networks, Physica D, 28 (1987), 305316.
 3. L. Duan, L. Huang, Z. Guo, et al. Periodic attractor for reactiondiffusion highorder hopfield neural networks with timevarying delays, Comput. Math. Appl., 73 (2017), 233245.
 4. J. Wang, X. Chen, L. Huang, The number and stability of limit cycles for planar piecewise linear systems of nodesaddle type, J. Math. Anal. Appl., 469 (2019), 405427.
 5. J. Wang, C. Huang, L. Huang, Discontinuityinduced limit cycles in a general planar piecewise linear system of saddlefocus type, Nonlinear Anal. Hybrid Syst., 33 (2019), 162178.
 6. Z. Cai, J. Huang, L. Huang, Periodic orbit analysis for the delayed Filippov system, P. Am. Math. Soc., 146 (2018), 46674682.
 7. T. Chen, L. Huang, P. Yu, et al. Bifurcation of limit cycles at infinity in piecewise polynomial systems, Nonlinear Anal. Real., 41 (2018), 82106.
 8. C. Huang, Y. Qiao, L. Huang, et al. Dynamical behaviors of a foodchain model with stage structure and time delays, Adv. Differ. Equ., 2018 (2018), 113.
 9. C. Huang, S. Wen, L. Huang, Dynamics of antiperiodic solutions on shunting inhibitory cellular neural networks with multiproportional delays, Neurocomputing, 357 (2019), 4752.
 10. Y. Ke, C. Miao, Stability and existence of periodic solutions in inertial BAM neural networks with time delay, Neural Comput. Appl., 23 (2013), 10891099.
 11. Y. Ke, C. Miao, Antiperiodic solutions of inertial neural networks with time delays, Neural Process. Lett., 45 (2017), 523538.
 12. C. Xu, Q. Zhang, Existence and global exponential stability of antiperiodic solutions for BAM neural networks with inertial term and delay, Neurocomputing, 153 (2015), 108116.
 13. C. Huang, B. Liu, New studies on dynamic analysis of inertial neural networks involving nonreduced order method, Neurocomputing, 325 (2019), 283287.
 14. X. Li, X. Li, C. Hu, Some new results on stability and synchronization for delayed inertial neural networks based on nonreduced order method, Neural Networks, 96 (2017), 91100.
 15. C. Huang, H. Zhang, Periodicity of nonautonomous inertial neural networks involving proportional delays and nonreduced order method, Int. J. Biomath., 12 (2019), 113.
 16. C. Huang, L. Yang, B. Liu, New results on periodicity of nonautonomous inertial neural networks involving nonreduced order method, Neural Process. Lett., 50 (2019), 595606.
 17. B. Liu, Antiperiodic solutions for forced Rayleightype equations, Nonlinear Anal. Real., 10 (2009), 28502856.
 18. J. M. Belley, E. Bondo, Antiperiodic solutions of Liénard equations with state dependent impulses, J. Differ. Equ., 261 (2016), 41644187.
 19. Z. Long, New results on antiperiodic solutions for SICNNs with oscillating coefficients in leakage terms, Neurocomputing, 171 (2016), 503509.
 20. C. Huang, Exponential stability of inertial neural networks involving proportional delays and nonreduced order method, J. Exp. Theor. Artif. Intell., 32 (2020), 133146.
 21. M. Zhang, D. Wang, Robust dissipativity analysis for delayed memristorbased inertial neural network, Neurocomputing, 366 (2019), 340351.
 22. M. Iswarya, R. Raja, G. Rajchakit, et al. Existence, uniqueness and exponential stability of periodic solution for discretetime delayed BAM neural networks based on coincidence degree theory and graph theoretic method, Mathematics, 7 (2019), 118.
 23. H. Zhang, Global Large Smooth Solutions for 3D Hallmagnetohydrodynamics, Discrete Contin. Dyn. Syst., 39 (2019), 66696682.
 24. X. Li, Z. Liu, J. Li, Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces, Acta Mech. Sin. Engl. Ser., 39 (2019), 229242.
 25. K. Zhu, Y. Xie, F. Zhou, Pullback attractors for a damped semilinear wave equation with delays, Acta Mech. Sin. Engl. Ser., 34 (2018), 11311150.
 26. J. Zhao, J. Liu, L. Fang, Antiperiodic boundary value problems of secondorder functional differential equations, Malays. Math. Sci. Soc., 37 (2014), 311320.
 27. X. Yang, S. Wen, Z. Liu, et al. Dynamic properties of foreign exchange complex network, Mathematics, 7 (2019), 119.
 28. N. Huo, B. Li, Y. Li, Existence and exponential stability of antiperiodic solutions for inertial quaternionvalued highorder Hopfield neural networks with statedependent delays, IEEE Access, 7 (2019), 6001060019.
 29. Z. X. Zheng, Theory of Functional Differential Equations, Heifei: Anhui Education Press, 1994.
 30. J. Li, J. Ying, D. Xie, On the analysis and application of an ion sizemodified PoissonBoltzmann equation, Nonlinear Anal. Real., 47 (2019), 188203.
 31. C. Huang, X. Long, J. Cao, Stability of antiperiodic recurrent neural networks with multiproportional delays, Math. Meth. Appl. Sci., 43 (2020), 60936102.
 32. J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equ., 120 (2020), 112.
 33. C. Huang, H. Yang, J. Cao, Weighted pseudo almost periodicity of multiproportional delayed shunting inhibitory cellular neural networks with D operator, Discrete Contin. Dyn. Syst. Ser. S, (2020), DOI:10.3934/dcdss.2020372.
 34. L. Yao, Global exponential stability on antiperiodic solutions in proportional delayed HIHNNs, J. Exp. Theor. Artif. Intell., (2020), 115.
 35. Y. Xu, Q. Cao, X. Guo, Stability on a patch structure Nicholson's blowflies system involving distinctive delays, Appl. Math. Lett., 105 (2020), 106340.
 36. W. Li, L. Huang, J. Ji, Periodic solution and its stability of a delayed BeddingtonDeAngelis type predatorprey system with discontinuous control strategy, Math. Meth. Appl. Sci., 42 (2019), 4498 4515.
 37. X. Gong, F. Wen, Z. He, et al. Extreme return, extreme volatility and investor sentiment, Filomat, 30 (2016), 39493961.
 38. C. Huang, L. Yang, J. Cao, Asymptotic behavior for a class of population dynamics, AIMS Mathematics, 5 (2020), 33783390.
 39. X. Long, S. Gong, New results on stability of Nicholson's blowflies equation with multiple pairs of timevarying delays, Appl. Math. Lett., 100 (2020), 106027.
 40. C. Huang, H. Zhang, L. Huang, Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear densitydependent mortality term, Commun. Pure Appl. Anal., 18 (2019), 33373349.
 41. C. Huang, C. Peng, X. Chen, et al. Dynamics analysis of a class of delayed economic model, Abstr. Appl. Anal., 2013 (2013), 112.
 42. C. Huang, H. Zhang, J. Cao, et al. Stability and Hopf bifurcation of a delayed preypredator model with disease in the predator, Int. J. Bifurcat. Chaos, 29 (2019), 1950091.
 43. C. Huang, X. Yang, J. Cao, Stability analysis of Nicholson's blowflies equation with two different delays, Math. Comput. Simulation, 171 (2020), 201206.
 44. 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), 18.
 45. Y. Zhou, X. Wan, C. Huang, et al. Finitetime stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control, Appl. Math. Comput., 376 (2020), 125157.
 46. X. Zhang, H. Hu, Convergence in a system of critical neutral functional differential equations, Appl. Math. Lett., 107 (2020), 106385.
 47. Y. Zhang, Some observations on the diophantine equation f(x)f(y)  f(z)(2), Colloq. Math., 142 (2016), 275283.
 48. C. Huang, R. Su, J. Cao, et al. Asymptotically stable highorder neutral cellular neural networks with proportional delays and D operators, Math. Comput. Simul., 171 (2020), 127135.
 49. C. Qian, New periodic stability for a class of Nicholson's blowflies models with multiple different delays, Int. J. Control, (2020), 113.
 50. L. Huang, H. Su, G. Tang, et al. Bilinear forms graphs over residue class rings, Linear Algebra Appl., 523 (2017), 1332.
 51. Q. Cao, G. Wang, C. Qian, New results on global exponential stability for a periodic Nicholson's blowflies model involving timevarying delays, delays, Adv. Differ. Equ., 2020 (2020), 112.
 52. C. Huang, X. Long, L. Huang, et al. Stability of almost periodic Nicholson's blowflies model involving patch structure and mortality terms, Canad. Math. Bull., 63 (2020), 405422.
 53. J. Peng, Y. Zhang, Heron triangles with figurate number sides, Acta Math. Hungar., 157 (2019), 478488.
 54. F. Wang, Z. Yao, Approximate controllability of fractional neutral differential systems with bounded delay, Fixed Point Theor., 17 (2016), 495507.
 55. W. Liu, An incremental approach to obtaining attribute reduction for dynamic decision systems, Open Math., 14 (2016), 875888.
 56. L. Huang, B. Lv, Cores and independence numbers of Grassmann graphs, Graphs Combin., 33 (2017), 16071620.
 57. L. Huang, J. Huang, K. Zhao, On endomorphisms of alternating forms graph, Discrete Math., 338 (2015), 110121.
 58. Y. Xu, Q. Cao, X. Guo, Stability on a patch structure Nicholson's blowflies system involving distinctive delays, Appl. Math. Lett., 105 (2020), 106340.
 59. 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), 57295749.
 60. L. Huang, B. Lv, K. Wang, The endomorphisms of Grassmann graphs, Ars Math. Contemp., 10 (2016), 383392.
 61. Y. Zhang, Right triangle and parallelogram pairs with a common area and a common perimeter, J. Number Theory, 164 (2016), 179190.
 62. H. Hu, L. Liu, Weighted inequalities for a general commutator associated to a singular integral operator satisfying a variant of Hormander's condition, Math. Notes, 101 (2017), 830840.
 63. L. Huang, B. Lv, K. Wang, ErdosKoRado theorem, Grassmann graphs and p(s)Kneser graphs for vector spaces over a residue class ring, J. Combin. Theory Ser. A, 164 (2019), 125158.
 64. Y. Li, M. Vuorinen, Q. Zhou, Characterizations of John spaces, Monatsh. Math, 188 (2019), 547 559.
 65. L. Li, Q. Jin, B. Yao, Regularity of fuzzy convergence spaces, Open Math., 16 (2018), 14551465.
 66. C. Huang, L. Liu, Boundedness of multilinear singular integral operator with nonsmooth kernels and mean oscillation, Quaest. Math., 40 (2017), 295312.
 67. C. Huang, J. Cao, F. Wen, et al. Stability analysis of SIR model with distributed delay on complex networks, PLoS One, 11 (2016), e0158813.
 68. X. Li, Y. Liu, J. Wu, Flocking and pattern motion in a modified cuckersmale model, Bull. Korean Math. Soc., 53 (2016), 13271339.
 69. Y. Xie, Q. Li, K. Zhu, Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity, Nonlinear Anal. Real., 31 (2016), 2337.
 70. Y. Xie, Y. Li, Y. Zeng, Uniform attractors for nonclassical diffusion equations with memory, J. Funct. Space., 2016 (2016), 111.
 71. F. Wang, P. Wang, Z. Yao, Approximate controllability of fractional partial differential equation, Adv. Differ. Equ., 2015 (2015), 110.
 72. Y. Liu, J. Wu, Multiple solutions of ordinary differential systems with minmax terms and applications to the fuzzy differential equations, Adv. Differ. Equ., 2015 (2015), 113, https://doi.org/10.1186/s136620150708z.
 73. L. Yan, J. Liu, Z. Luo, Existence and multiplicity of solutions for secondorder impulsive differential equations on the halfline, Adv. Differ. Equ., 2013 (2013), 112.
 74. Y. Liu, J. Wu, Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems, Math. Meth. Appl. Sci., 37 (2014), 508517.
 75. D. Tong, W. Wang, Conditional regularity for the 3D MHD equations in the critical Besov space, Appl. Math. Lett., 102 (2020), 106119.
 76. Y. Cai, K. Wang, W. Wang, Global transmission dynamics of a Zika virus model, Appl. Math. Lett., 92 (2019), 190195.
 77. C. Huang, J. Wang, L. Huang, Asymptotically almost periodicity of delayed Nicholsontype system involving patch structure, Electron. J. Differ. Equ., 2020 (2020), 117.
 78. H. Zhang, Q. Cao, H. Yang, Asymptotically almost periodicity of delayed Nicholsontype system involving patch structure, J. Inequal. Appl., 2020 (2020), 127.
 79. C. Qian, Y. Hu, Novel stability criteria on nonlinear densitydependent mortality Nicholson's blowflies systems in asymptotically almost periodic environments, J. Inequal. Appl., 2020 (2020), 118.
 80. S. Zhou, Y. Jiang, Finite volume methods for Ndimensional time fractional FokkerPlanck equations, Bull. Malays. Math. Sci. Soc., 42 (2019), 31673186.
 81. C. Huang, S. Wen, M. Li, et al. An empirical evaluation of the influential nodes for stock market network: Chinese A shares case, Financ. Res. Lett., (2020), 101517.
 82. L. Huang, Endomorphisms and cores of quadratic forms graphs in odd characteristic, Finite Fields Appl., 55 (2019), 284304.
This article has been cited by:
 1. Qian Cao, Xin Long, New convergence on inertial neural networks with timevarying delays and continuously distributed delays, AIMS Mathematics, 2020, 5, 6, 5955, 10.3934/math.2020381
 2. Luogen Yao, Qian Cao, Antiperiodicity on highorder inertial Hopfield neural networks involving mixed delays, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660020024443
 3. Xin Long, Novel stability criteria on a patch structure Nicholson’s blowflies model with multiple pairs of timevarying delays, AIMS Mathematics, 2020, 5, 6, 7387, 10.3934/math.2020473
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