Citation: Qian Cao, Xiaojin Guo. Anti-periodic dynamics on high-order inertial Hopfield neural networks involving time-varying delays[J]. AIMS Mathematics, 2020, 5(6): 5402-5421. doi: 10.3934/math.2020347
[1] | K. Babcock, R. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Physica D, 23 (1986), 464-469. |
[2] | K. Babcock, R. Westervelt, Dynamics of simple electronic neural networks, Physica D, 28 (1987), 305-316. |
[3] | 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. |
[4] | 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. |
[5] | 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. |
[6] | Z. Cai, J. Huang, L. Huang, Periodic orbit analysis for the delayed Filippov system, P. Am. Math. Soc., 146 (2018), 4667-4682. |
[7] | T. Chen, L. Huang, P. Yu, et al. Bifurcation of limit cycles at infinity in piecewise polynomial systems, Nonlinear Anal. Real., 41 (2018), 82-106. |
[8] | C. Huang, Y. Qiao, L. Huang, et al. Dynamical behaviors of a food-chain model with stage structure and time delays, Adv. Differ. Equ., 2018 (2018), 1-13. |
[9] | C. Huang, S. Wen, L. Huang, Dynamics of anti-periodic solutions on shunting inhibitory cellular neural networks with multi-proportional delays, Neurocomputing, 357 (2019), 47-52. |
[10] | Y. Ke, C. Miao, Stability and existence of periodic solutions in inertial BAM neural networks with time delay, Neural Comput. Appl., 23 (2013), 1089-1099. |
[11] | Y. Ke, C. Miao, Anti-periodic solutions of inertial neural networks with time delays, Neural Process. Lett., 45 (2017), 523-538. |
[12] | 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. |
[13] | C. Huang, B. Liu, New studies on dynamic analysis of inertial neural networks involving nonreduced order method, Neurocomputing, 325 (2019), 283-287. |
[14] | 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. |
[15] | C. Huang, H. Zhang, Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method, Int. J. Biomath., 12 (2019), 1-13. |
[16] | C. Huang, L. Yang, B. Liu, New results on periodicity of non-autonomous inertial neural networks involving non-reduced order method, Neural Process. Lett., 50 (2019), 595-606. |
[17] | B. Liu, Anti-periodic solutions for forced Rayleigh-type equations, Nonlinear Anal. Real., 10 (2009), 2850-2856. |
[18] | J. M. Belley, E. Bondo, Anti-periodic solutions of Liénard equations with state dependent impulses, J. Differ. Equ., 261 (2016), 4164-4187. |
[19] | Z. Long, New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms, Neurocomputing, 171 (2016), 503-509. |
[20] | C. Huang, Exponential stability of inertial neural networks involving proportional delays and nonreduced order method, J. Exp. Theor. Artif. Intell., 32 (2020), 133-146. |
[21] | M. Zhang, D. Wang, Robust dissipativity analysis for delayed memristor-based inertial neural network, Neurocomputing, 366 (2019), 340-351. |
[22] | M. Iswarya, R. Raja, G. Rajchakit, et al. Existence, uniqueness and exponential stability of periodic solution for discrete-time delayed BAM neural networks based on coincidence degree theory and graph theoretic method, Mathematics, 7 (2019), 1-18. |
[23] | H. Zhang, Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics, Discrete Contin. Dyn. Syst., 39 (2019), 6669-6682. |
[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), 229-242. |
[25] | K. Zhu, Y. Xie, F. Zhou, Pullback attractors for a damped semilinear wave equation with delays, Acta Mech. Sin. Engl. Ser., 34 (2018), 1131-1150. |
[26] | J. Zhao, J. Liu, L. Fang, Anti-periodic boundary value problems of second-order functional differential equations, Malays. Math. Sci. Soc., 37 (2014), 311-320. |
[27] | X. Yang, S. Wen, Z. Liu, et al. Dynamic properties of foreign exchange complex network, Mathematics, 7 (2019), 1-19. |
[28] | N. Huo, B. Li, Y. Li, Existence and exponential stability of anti-periodic solutions for inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays, IEEE Access, 7 (2019), 60010-60019. |
[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 size-modified Poisson-Boltzmann equation, Nonlinear Anal. Real., 47 (2019), 188-203. |
[31] | C. Huang, X. Long, J. Cao, Stability of anti-periodic recurrent neural networks with multiproportional delays, Math. Meth. Appl. Sci., 43 (2020), 6093-6102. |
[32] | J. Zhang, C. Huang, Dynamics analysis on a class of delayed neural networks involving inertial terms, Adv. Differ. Equ., 120 (2020), 1-12. |
[33] | 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, (2020), DOI:10.3934/dcdss.2020372. doi: 10.3934/dcdss.2020372 |
[34] | L. Yao, Global exponential stability on anti-periodic solutions in proportional delayed HIHNNs, J. Exp. Theor. Artif. Intell., (2020), 1-15. |
[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 Beddington-DeAngelis type predator-prey 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), 3949-3961. |
[38] | C. Huang, L. Yang, J. Cao, Asymptotic behavior for a class of population dynamics, AIMS Mathematics, 5 (2020), 3378-3390. |
[39] | 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. |
[40] | 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. |
[41] | C. Huang, C. Peng, X. Chen, et al. Dynamics analysis of a class of delayed economic model, Abstr. Appl. Anal., 2013 (2013), 1-12. |
[42] | 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. 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), 201-206. |
[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), 1-8. |
[45] | 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. |
[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), 275-283. |
[48] | C. Huang, R. Su, J. Cao, et al. Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators, Math. Comput. Simul., 171 (2020), 127-135. |
[49] | C. Qian, New periodic stability for a class of Nicholson's blowflies models with multiple different delays, Int. J. Control, (2020), 1-13. |
[50] | L. Huang, H. Su, G. Tang, et al. Bilinear forms graphs over residue class rings, Linear Algebra Appl., 523 (2017), 13-32. |
[51] | Q. Cao, G. Wang, C. Qian, New results on global exponential stability for a periodic Nicholson's blowflies model involving time-varying delays, delays, Adv. Differ. Equ., 2020 (2020), 1-12. |
[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), 405-422. |
[53] | J. Peng, Y. Zhang, Heron triangles with figurate number sides, Acta Math. Hungar., 157 (2019), 478-488. |
[54] | F. Wang, Z. Yao, Approximate controllability of fractional neutral differential systems with bounded delay, Fixed Point Theor., 17 (2016), 495-507. |
[55] | W. Liu, An incremental approach to obtaining attribute reduction for dynamic decision systems, Open Math., 14 (2016), 875-888. |
[56] | L. Huang, B. Lv, Cores and independence numbers of Grassmann graphs, Graphs Combin., 33 (2017), 1607-1620. |
[57] | L. Huang, J. Huang, K. Zhao, On endomorphisms of alternating forms graph, Discrete Math., 338 (2015), 110-121. |
[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), 5729-5749. |
[60] | L. Huang, B. Lv, K. Wang, The endomorphisms of Grassmann graphs, Ars Math. Contemp., 10 (2016), 383-392. |
[61] | Y. Zhang, Right triangle and parallelogram pairs with a common area and a common perimeter, J. Number Theory, 164 (2016), 179-190. |
[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), 830-840. |
[63] | 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. |
[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), 1455-1465. |
[66] | C. Huang, L. Liu, Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation, Quaest. Math., 40 (2017), 295-312. |
[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 cucker-smale model, Bull. Korean Math. Soc., 53 (2016), 1327-1339. |
[69] | Y. Xie, Q. Li, K. Zhu, Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity, Nonlinear Anal. Real., 31 (2016), 23-37. |
[70] | Y. Xie, Y. Li, Y. Zeng, Uniform attractors for nonclassical diffusion equations with memory, J. Funct. Space., 2016 (2016), 1-11. |
[71] | F. Wang, P. Wang, Z. Yao, Approximate controllability of fractional partial differential equation, Adv. Differ. Equ., 2015 (2015), 1-10. |
[72] | 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, https://doi.org/10.1186/s13662-015-0708-z. |
[73] | 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. |
[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), 508-517. |
[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), 190-195. |
[77] | 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. |
[78] | H. Zhang, Q. Cao, H. Yang, Asymptotically almost periodicity of delayed Nicholson-type system involving patch structure, J. Inequal. Appl., 2020 (2020), 1-27. |
[79] | 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. |
[80] | S. Zhou, Y. Jiang, Finite volume methods for N-dimensional time fractional Fokker-Planck equations, Bull. Malays. Math. Sci. Soc., 42 (2019), 3167-3186. |
[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), 284-304. |