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中文核心期刊
Zhang Shu, Xu Jian. REVIEW ON NONLINEAR DYNAMICS IN SYSTEMS WITH COULPLING DELAYS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 565-587. DOI: 10.6052/0459-1879-17-123
Citation: Zhang Shu, Xu Jian. REVIEW ON NONLINEAR DYNAMICS IN SYSTEMS WITH COULPLING DELAYS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 565-587. DOI: 10.6052/0459-1879-17-123

REVIEW ON NONLINEAR DYNAMICS IN SYSTEMS WITH COULPLING DELAYS

  • Received Date: April 12, 2017
  • Available Online: April 20, 2017
  • With the deep understanding towards the objective laws of nature, requirements on refinement and complexity in engineering system design are increasing. Many coupled dynamic system designs need to take into account the dynamics induced by the time delay existing in the coupling process. Such coupling time delay may come from the process of coupling with the sensing system, the actuation system and the control system. Coupling delays also extensively exist in the fields such as transportation system, system biology, electronic communication, neural and information networks and etc. Firstly, based on the concept of coupling delay, this paper reviews the recent research progresses on dynamics induced by such delay from the following four aspects: (1) the delay-centered mechanism of complex dynamics in coupled systems; (2) experimental foundation and realization of stabilizing coupled systems by utilizing time delay; (3) dynamics of fast-slow coupled system with time delay; and (4) synchronization and desynchronization of delayed neural networks. Some advances in the general theory of systems with coupling delay are highlighted including the coupling-delay-induced bifurcation and singularity with high codimention and the novel quantitative method of analysis, normal form computation for neutral delay differential equations, identification of time delay and nonlinear parameters in nonlinear systems with coupling delay and the relevant experiment, relaxation oscillation in the fast-slow system with coupling delay, and transition of modes of synchronization induced by coupling delay in network systems. Secondly, as for the application, some new results are presented in details such as the coupling-delay-induced chatter in grinding process and its mechanism, bifurcation with high codimension and complex dynamics induced by coupling delay in neural networks with inertial terms, and design and experiments of vibration absorber and isolator using coupling delay. Finally, some problems which are worthy of attention in near future are highlighted from perspectives of the general theory of systems with coupling delay and the potential applications.
  • [1]
    Xu J, Chung KW. Dynamics for a class of nonlinear systems with time delay. Chaos, Solitons and Fractals, 2009, 40(1):28-49 doi: 10.1016/j.chaos.2007.07.032
    [2]
    胡海岩, 王在华.非线性时滞动力系统的研究进展.力学进展, 1999, 29:501-512 doi: 10.6052/1000-0992-1999-4-J1998-103

    Hu Haiyan, Wang Zaihua. Review on nonlinear dynamic systems involving time delays. Advances in Mechanics, 1999, 29:501-512 (in Chinese) doi: 10.6052/1000-0992-1999-4-J1998-103
    [3]
    徐鉴, 裴利军.时滞系统动力学近期研究进展与展望.力学进展, 2006, 36:17-30 doi: 10.6052/1000-0992-2006-1-J2005-095

    Xu Jian, Pei Lijun. Advances in dynamics for delayed systems. Advances in Mechanics, 2006, 36:17-30 (in Chinese) doi: 10.6052/1000-0992-2006-1-J2005-095
    [4]
    Liu ZH, Payre G. Stability analysis of doubly regenerative cylindrical grinding process. Journal of Sound and Vibration, 2007, 301(3-5):950-962 doi: 10.1016/j.jsv.2006.10.041
    [5]
    Sipahi R, Atay FM, Niculescu SI. Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers. SIAM Journal of Applied Mathematics, 2007, 68(3-5):738-759 https://www.researchgate.net/publication/45062660_Stability_of_Traffic_Flow_Behavior_with_Distributed_Delays_Modeling_the_Memory_Effects_of_the_Drivers
    [6]
    王在华, 胡海岩.时滞动力系统的稳定性与分岔:从理论走向应用.力学进展, 2013, 43(1):3-19 doi: 10.6052/1000-0992-12-018

    Wang Zaihua, Hu Haiyan. Stability and bifurcation of delayed dynamic systems:from theory to application. Advances in Mechanics, 2013, 43(1):3-19 (in Chinese) doi: 10.6052/1000-0992-12-018
    [7]
    徐鉴.振动控制研究进展综述.力学季刊, 2015, 36(4):547-565 http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX201504001.htm

    Xu Jian. Advances of research on vibration control. Chinese Quarterly of Mechanics, 2015, 36(4):547-565 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX201504001.htm
    [8]
    Erzgraber E, Krauskopf B, Lenstra D. Bifurcation analysis of a semiconductor laser with filtered optical feedback. SIAM Journal of Applied systems, 2007, 6(1):1-28 doi: 10.1137/060656656
    [9]
    Green K. Stability near threshold in a semiconductor laser subject to optical feedback:a bifurcation analysis of the Lang-Kobayashi equations. Physical Review E, 2009, 79(3):036210 doi: 10.1103/PhysRevE.79.036210
    [10]
    Campbell SA, Yuan Y. Zero singularities of codimension two and three in delay differential equations. Nonlinearity, 2008, 21(11):2671-2691 doi: 10.1088/0951-7715/21/11/010
    [11]
    Xu J, Chung KW. A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems. Science in China Series E, 2009, 52(3):698-708 doi: 10.1007/s11431-009-0052-1
    [12]
    Xu J, Chung KW. An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks. SIAM Journal on Applied Systems, 2007, 6(1):29-60 doi: 10.1137/040614207
    [13]
    Xu J, Chung KW. Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities. Mathematical Problems in Engineering, 2009, 2009(4):266-287 https://www.researchgate.net/publication/40892243_Double_Hopf_Bifurcation_with_Strong_Resonances_in_Delayed_Systems_with_Nonlinerities
    [14]
    Liu ZH, Zhu WQ. Compensation for time-delayed feedback bangbang control of quasi-integrable Hamiltonian systems. Science in China Series E, 2009, 52(3):688-697 doi: 10.1007/s11431-009-0035-2
    [15]
    Zhen B, Xu J. Fold-Hopf bifurcation analysis for a coupled FitzHugh-Nagumo neural system with time delay. International Journal of Bifurcation and Chaos, 2010, 20(12):3919-3914 doi: 10.1142/S0218127410028112
    [16]
    Wang WY, Xu J. Multiple scales analysis for double Hopf Bifurcation with 1:3 resonance. Nonlinear Dynamics, 2011, 66(1-2):39-51 doi: 10.1007/s11071-010-9909-x
    [17]
    Wang WY, Xu J. Strong and weak resonances in delayed differential systems. International Journal of Bifurcation and Chaos, 2013, 23(7):1350119 doi: 10.1142/S0218127413501198
    [18]
    Song ZG, Xu J. Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays. Cognitive Neurodynamics, 2013, 7(6):505-521 doi: 10.1007/s11571-013-9254-0
    [19]
    Song YL, Han Y, Peng Y. Stability and Hopf bifurcation in an unidirectional ring of n neurons with distributed delays. Neurocomputing, 2013, 121(2):442-452 https://www.researchgate.net/publication/257633383_Stability_and_Hopf_bifurcation_in_a_three-neuron_unidirectional_ring_with_distributed_delays
    [20]
    Chen YL, Xu J. Applications of the integral equation method to delay differential equations. Nonlinear Dynamics, 2013, 73(4):2241-2260 doi: 10.1007/s11071-013-0938-0
    [21]
    Li JY, Zhang L, Wang ZH. A simple algorithm for the stability testing of periodic solutions of some nonlinear oscillators with large time-delay. Science in China Series E:Technological Sciences, 2011, 54(8):2033-2043 doi: 10.1007/s11431-011-4487-9
    [22]
    Wang ZH. A very simple criterion for characterizing the crossing direction of time-delay systems with delay-dependent parameters. International Journal of Bifurcation and Chaos, 2012, 22(3):1250048 doi: 10.1142/S0218127412500484
    [23]
    Zhang L, Wang HL, Hu HY. Symbolic computation of normal form for Hopf bifurcation in a retarded functional differential equation with unknown parameters. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(8):3328-3344 doi: 10.1016/j.cnsns.2011.11.035
    [24]
    Zhang L, Wang HL, Wang ZH. Symbolic computation of normal form for Hopf bifurcationin a neutral delay differential equation and an applicationto a controlled crane. Nonlinear Dynamics, 2012, 70(1):463-473 doi: 10.1007/s11071-012-0468-1
    [25]
    Yan Y, Xu J, Wang WY. Nonlinear chatter with large amplitude in a cylindrical plunge grinding process. Nonlinear Dynamics, 2012, 69(4):1781-1793 doi: 10.1007/s11071-012-0385-3
    [26]
    Yan Y, Xu J, Wiercigroch M. Chatter in a transverse grinding process. Journal of Sound and Vibration, 2014, 333(3):937-953 doi: 10.1016/j.jsv.2013.09.039
    [27]
    Ge JH, Xu J. Hopf bifurcation and chaos in an inertial neuron system with coupled delay. Science China:Technological Sciences, 2013, 56(9):2299-2309 doi: 10.1007/s11431-013-5316-0
    [28]
    Ge JH, Xu J. Weak resonant double Hopf bifurcations in an inertial four-neuron model with time delay. International Journal of Neural Systems, 2012, 22(1):63-75 doi: 10.1142/S0129065712002980
    [29]
    Ge JH, Xu J. Stability switches and fold-Hopf bifurcations in an inertial four-neuron network model with coupling delay. Neurocomputing, 2013, 110(8):70-79 https://www.researchgate.net/publication/257352421_Stability_switches_and_fold-Hopf_bifurcations_in_an_inertial_four-neuron_network_model_with_coupling_delay
    [30]
    Jiang J, Song YL. Bogdanov-Takens bifurcation in an oscillator with negative damping and delayed position feedback. Applied Mathematical Modelling, 2013, 37(16-17):8091-8105 doi: 10.1016/j.apm.2013.03.034
    [31]
    Song ZG, Xu J. Stability switches and Bogdanov-Takens bifurcation in an inertial two-neurons coupling system with multiple delays. Science China:Technological Sciences, 2014, 57(5):893-904 doi: 10.1007/s11431-014-5536-y
    [32]
    Song ZG, Xu J. Codimension-two bursting analysis in the delayed neural system with external stimulations. Nonlinear Dynamics, 2012, 67(1):309-328 doi: 10.1007/s11071-011-9979-4
    [33]
    Song ZG, Xu J. Stability switches and multistability coexistence in a delay-coupled neural oscillators system. Journal of Theoretical Biology, 2012, 313(21):98-114 http://cpfd.cnki.com.cn/Article/CPFDTOTAL-AGLU201205003347.htm
    [34]
    徐鉴, 陈振.时滞对轴流压气机喘振的影响.中国科学:物理学力学天文学, 2013, 43(4):380-389 http://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201304006.htm

    Xu Jian, Chen Zhen. Effects of delay on surge in axial compressors. Science in China (Series G), 2013, 43(4):380-389(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201304006.htm
    [35]
    Zhen B, Xie WP, Xu J. A nonlinear analysis for the lateral vibration of footbridges induced by pedestrians. ASCE:Journal of Bridge Engineering, 2013, 18(2):122-130 doi: 10.1061/(ASCE)BE.1943-5592.0000313
    [36]
    Zhen B, Wong WK, Xu J, et al. Application of Nakamura's model to describe the delayed increase in lateral vibration of footbridges. ASCE:Journal of Engineering Mechanics, 2012, 139(12):1708-1713 https://www.researchgate.net/publication/229147445_Parametric_resonance_of_flexible_footbridges_under_crowd-induced_lateral_excitation
    [37]
    Zhen B, Luo W, Xu J. Analysis of critical velocities for an infinite timoshenko beam resting on an elastic foundation subjected to a harmonic moving load. Shock and Vibration, 2014, 2014(2):848536 https://www.researchgate.net/profile/Bin_Zhen2/publication/267028895_Analysis_of_Critical_Velocities_for_an_Infinite_Timoshenko_Beam_Resting_on_an_Elastic_Foundation_Subjected_to_a_Harmonic_Moving_Load/links/547cba5b0cf2cfe203c1fba3.pdf?disableCoverPage=true
    [38]
    Hu HY. Using delayed state feedback to stabilize periodic motions of an oscillator. Journal of Sound and Vibration, 2004, 275(s3-5):1009-1025 https://www.researchgate.net/publication/256799922_Using_delayed_state_feedback_to_stabilize_periodic_motions_of_an_oscillator
    [39]
    Xu J, Chung KW. Effects of time delayed position feedback on a van der Pol-Duffing oscillator. Physica D, 2003, 180(1-2):17-39 doi: 10.1016/S0167-2789(03)00049-6
    [40]
    Liu B, Hu HY. Group delay induced instabilities and Hopf bifurcations of a controlled double pendulum. International Journal of Non-Linear Mechanics, 2010, 45(4):442-452 doi: 10.1016/j.ijnonlinmec.2010.01.001
    [41]
    Ohta T, Murakami T. A Stabilization control of bilateral system with time delay by vibration index-application to inverted pendulum Control. IEEE Transactions on Industrial Electronics, 2009, 56(5):1595-1603 doi: 10.1109/TIE.2008.2009991
    [42]
    Landry M, Campbell SA, Morris K, et al. Dynamics of an inverted pendulum with delayed feedback control. SIAM Journal on Applied Dynamical Systems, 2005, 4(2):333-351 doi: 10.1137/030600461
    [43]
    Campbell SA, Crawford S, Morris K. Friction and the inverted pendulum stabilization problem. Journal of Dynamic Systems Measurement and Control, 2008, 130(5):054502 doi: 10.1115/1.2957631
    [44]
    Olgac N, Holm-Hansen BT. A novel active vibration absorption technique:delayed resonator. Journal of Sound and Vibration, 1994, 176(1):93-104 doi: 10.1006/jsvi.1994.1360
    [45]
    Filipović D, Olgac N. Delayed resonator with speed feedback including dual frequency-theory and experiments//Proceedings of the 36th Conference on Decision & Control, 1997:2535-2540
    [46]
    赵艳影, 徐鉴.时滞动力吸振器及其对主系统振动的影响.振动工程学报, 2006, 19(4):548-552 http://www.cnki.com.cn/Article/CJFDTOTAL-GXKZ201602012.htm

    Zhao Yanying, Xu Jian. Delayed resonator and its effects on vibrations in primary system. Journal of Vibration Engineering, 2006, 19(4):548-552(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXKZ201602012.htm
    [47]
    Zhao YY, Xu J. Effects of delayed feedback control on nonlinear vibration absorber system. Journal of Sound and Vibration, 2007, 308:212-230 doi: 10.1016/j.jsv.2007.07.041
    [48]
    赵艳影, 徐鉴.时滞非线性动力吸振器的减振机理.力学学报, 2008, 40(1):98-106 doi: 10.6052/0459-1879-2008-1-2007-078

    Zhao Yanying, Xu Jian. Mechanism analysis of delayed nonlinear vibration absorber. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(1):98-106(in Chinese) doi: 10.6052/0459-1879-2008-1-2007-078
    [49]
    Zhang XX, Xu J. Identification of time delay in nonlinear systems with delayed feedback control. Journal of the Franklin Institute, 2015, 352(8):2987-2998 doi: 10.1016/j.jfranklin.2014.04.016
    [50]
    Zhang XX, Xu J, Huang Y. Experiment on parameter identification of a time delayed vibration absorber. IFAC Papersonline, 2015, 48(12):57-62 doi: 10.1016/j.ifacol.2015.09.353
    [51]
    Zhang X, Xu J, Feng Z. Nonlinear equivalent model and its identification for a delayed absorber with magnetic action using distorted measurement. Nonlinear Dynamics, 2017, 88(2):937-954 doi: 10.1007/s11071-016-3286-z
    [52]
    Sun YX, Xu J. Experiments and analysis for a controlled mechanical absorber considering delay effect. Journal of Sound and Vibration, 2015, 339:25-37 doi: 10.1016/j.jsv.2014.11.005
    [53]
    Xu J, Sun YX. Experimental studies on active control of a dynamic system via a time-delayed absorber. Acta Mechanica Sinica, 2015, 31(2):229-247 doi: 10.1007/s10409-015-0411-z
    [54]
    Sun XT, Xu J, Jing XJ, et al. Beneficial performance of a quasi-zerostiffness vibration isolator with time-delayed active control. International Journal of Mechanical Science, 2014, 82(1):32-40 https://www.researchgate.net/publication/260608904_Beneficial_Performance_of_a_Quasi-Zero-Stiffness_Vibration_Isolator_with_Time-Delayed_Active_Control
    [55]
    Sun XT, Jing XJ, Xu J, et al. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 2014, 333(9):2404-2420 doi: 10.1016/j.jsv.2013.12.025
    [56]
    Sun XT, Jing XJ, Xu J, et al. A quasi-zero-stiffness-based sensor system in vibration measurement. IEEE Transactions on Industrial Electronics, 2014, 61(10):5606-5614 doi: 10.1109/TIE.2013.2297297
    [57]
    Sun XT, Jing XJ, Xu J, et al. A 3D quasi-zero-stiffness based sensor system for absolute motion measurement and application in active vibration control. IEEE/ASME Transactions on Mechatronics, 2015, 20(1):254-262 doi: 10.1109/TMECH.2014.2338932
    [58]
    Song ZG, Xu J. Bifurcation and chaos analysis on a delayed twoneural network with the variation slope ratio in activation function. International Journal of Bifurcation and Chaos, 2012, 22(5):1250105 doi: 10.1142/S0218127412501052
    [59]
    Zhao YY, Xu J. Using the delayed feedback control and saturation control to suppress the vibration of the dynamical system. Nonlinear Dynamics, 2012, 67:735-753 doi: 10.1007/s11071-011-0023-5
    [60]
    赵艳影, 徐鉴.利用时滞反馈控制自参数振动系统的振动.力学学报, 2011, 43 (5):894-904 doi: 10.6052/0459-1879-2011-5-lxxb2010-652

    Zhao Yanying, Xu Jian. Using the delayed feedback to control the vibration of the auto-parametric dynamical system. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5):894-904(in Chinese) doi: 10.6052/0459-1879-2011-5-lxxb2010-652
    [61]
    Yan Y, Xu J. Suppression of regenerative chatter in a plungegrinding process by spindle speed. Journal of Manufacturing Science & Engineering, 2013, 135(4):041019 https://www.researchgate.net/publication/259192519_Suppression_of_Regenerative_Chatter_in_a_Plunge-Grinding_Process_by_Spindle_Speed
    [62]
    Zhang S, Xu J. Time-vary delayed feedback control for an Internet congestion control model. Discrete and Continuous Dynamical Systems-Series B, 2011, 2(2):653-668 https://www.researchgate.net/publication/267076138_Time-varying_delayed_feedback_control_for_an_internet_congestion_control_model
    [63]
    Zhang S, Xu J. Oscillation control for n-dimensional congestion control model via time-varying delay. Science in China Series E:Technological Sciences, 2011, 54(8):2044-2053 doi: 10.1007/s11431-011-4488-8
    [64]
    Zhang S, Xu J. Bursting-like motion induced by time-varying delay in an internet congestion control model. Acta Mechanica Sinica, 2012, 28(4):1169-1179 doi: 10.1007/s10409-012-0128-1
    [65]
    Zhang S, Xu J. Oscillatory dynamics induced by time delay in an internet congestion control model with ring topology. Applied Mathematics and Computation, 2012, 281(22):11033-11041 https://www.researchgate.net/publication/256936669_Oscillatory_dynamics_induced_by_time_delay_in_an_internet_congestion_control_model_with_ring_topology
    [66]
    Zhang S, Xu J. Quasiperiodic motion induced by heterogeneous delays in a simplified internet congestion control model. Nonlinear Analysis:Real World Applications, 2013, 14(1):661-670 doi: 10.1016/j.nonrwa.2012.07.024
    [67]
    Zhang S, Chung KW, Xu J. Stability switch boundaries in an internet congestion control model with diverse time delays. International Journal of Bifurcation and Chaos, 2013, 23(5):1330016 doi: 10.1142/S0218127413300164
    [68]
    Zhang S, Xu J. On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function. Communications in Nonlinear Science and Numerical Simulation, 2015, 22(1-3):269-284 doi: 10.1016/j.cnsns.2014.09.020
    [69]
    Zhou YS, Wang ZH. Optimal feedback control for linear systems with input delays revisited. Journal of Optimization Theory and Applications, 2014, 163(3):989-1017 doi: 10.1007/s10957-014-0532-8
    [70]
    朱霖河, 赵洪涌.时滞惯性神经网络的稳定性和分岔控制.物理学报, 2014, 63(9):090203 http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201409004.htm

    Zhu Linhe, Zhao Hongyong. Stability and bifurcation control in inertial neuron networks with delays. Acta Physica Sinica, 2014, 63(9):090203 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201409004.htm
    [71]
    郑远广, 王在华.含时滞的快——慢耦合系统的动力学研究进展.力学进展, 2011, 41:400-410 doi: 10.6052/1000-0992-2011-4-lxjzJ2009-019

    Zheng Yuanguang, Wang Zaihua. Advances in dynamics of slow-fast systems with time delay. Advances in Mechanics, 2011, 41:400-410(in Chinese) doi: 10.6052/1000-0992-2011-4-lxjzJ2009-019
    [72]
    England JP, Krauskopf B, Osinga HM. Computing two-dimensional global invariant manifolds in slow-fast systems. International Journal of Bifurcation and Chaos, 2007, 17(3):805-822 doi: 10.1142/S0218127407017562
    [73]
    Branicki M, Wiggins S. An adaptive method for computing invariant manifolds in non-autonomous, three-dimensional dynamical systems. Physica D, 2009, 238(16):1625-1657 doi: 10.1016/j.physd.2009.05.005
    [74]
    Vakakis AF, Rand RH. Nonlinear dynamics of a system of coupled oscillators with essential stiffness nonlinearities. International Journal of Non-Linear Mechanics, 2004, 39(7):1079-1091 doi: 10.1016/S0020-7462(03)00098-2
    [75]
    Pirbodaghi T, Hoseini S. Nonlinear free vibration of a symmetrically conservative two-mass system with cubic nonlinearity. Journal of Computation and Nonlinear Dynamics, 2009, 5(1):011006 https://www.researchgate.net/publication/265361125_Free_oscillations_of_a_nonlinear_cubic_system_with_two_degrees_of_freedom_and_close_natural_frequencies
    [76]
    Lee YS, Vakakis AF, Bergman LA, et al. Passive non-linear targeted energy transfer and its applications to vibration absorption:A review. Journal of Multi-body Dynamics, 2008, 222(2):77-134 https://www.researchgate.net/publication/225356821_Robustness_of_nonlinear_targeted_energy_transfer_in_coupled_oscillators_to_changes_of_initial_conditions
    [77]
    Laxalde D, Thouverez F, Sinou JJ. Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber. International Journal of Nonlinear Mechanics, 2006, 41(8):969-978 doi: 10.1016/j.ijnonlinmec.2006.09.002
    [78]
    Zheng YG, Wang ZH. Stability and Hopf-bifurcation of a class of TCP/AQM networks. Nonlinear Analysis:Real World Applications, 2010, 11(11):1552-1559 https://www.researchgate.net/publication/242999642_Stability_and_Hopf_bifurcation_of_a_class_of_TCPAQM_networks
    [79]
    Zheng YG, Wang ZH. Delayed Hopf-bifurcation in time-delayed slow-fast systems. Science China Technological Sciences, 2010, 53(2):656-663 http://www.cnki.com.cn/Article/CJFDTOTAL-JEXG201003008.htm
    [80]
    Jiang SY, Xu J, Yan Y. Stability and oscillations in a fast-slow flexible joint system with transformation delay. Acta Mechanica Sinica, 2014, 30(5):727-738 doi: 10.1007/s10409-014-0064-3
    [81]
    Xu J, Jiang SY. Delay-induced Bogdanov-Takens bifurcation and dynamical classifications in a slow-fast flexible joint system. International Journal of Bifurcation and Chaos, 2015, 25(9):1550121 doi: 10.1142/S0218127415501217
    [82]
    郑远广, 黄承代, 王在华.反馈时滞对van der Pol振子张弛振荡的影响.力学学报, 2012, 44(1):148-157 doi: 10.6052/0459-1879-2012-1-lxxb2011-244

    Zheng Yuanguang, Huang Chengdai, Wang Zaihua. Delay effect on the relaxasion oscillations of a van der pol oscillator with delayed feedback. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(1):148-157(in Chinese) doi: 10.6052/0459-1879-2012-1-lxxb2011-244
    [83]
    Zheng YG, Wang ZH. Stability analysis of nonlinear dynamic systems with slowly and periodically varying delay. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(10):3999-4009 doi: 10.1016/j.cnsns.2012.02.026
    [84]
    Zheng YG, Wang ZH. Relaxation oscillation and attractive basins of a two-neuron Hopfield network with slow and fast variables. Nonlinear Dynamics, 2012, 70(2):1231-1240 doi: 10.1007/s11071-012-0527-7
    [85]
    Zheng YG, Wang ZH. Time-delay effect on the bursting of the synchronized state of coupled Hindmarsh-Rose neurons.Chaos, 2012, 22:043127 doi: 10.1063/1.4768664
    [86]
    Pare D, Curro'Dossi R, Steriade M. Neuronal basis of the Parkinsonian resting tremor:A hypothesis and its implications for treatment. Neuroscience, 1990, 35(2):217-226 doi: 10.1016/0306-4522(90)90077-H
    [87]
    Feng CF, Zhang Y, Sun JT, et al. Generalized projective synchronization in time-delayed chaotic systems. Chaos, Solitons and Fractal, 2008, 38(3):743-747 doi: 10.1016/j.chaos.2007.01.037
    [88]
    Ghosh D. Generalized projective synchronization in time-delayed systems:Nonlinear observer approach. Chaos, 2009, 19:013102 doi: 10.1063/1.3054711
    [89]
    Fridman E, Shaked U. H-infinity control of linear state-delay descriptor systems:An LMI approach. Linear Algebra Application, 2002, 351-352:271-302 doi: 10.1016/S0024-3795(01)00563-8
    [90]
    Wang QY, Lu QS. Phase synchronization in small world chaotic neural networks. Chinese Physical Letter, 2005, 22(6):1329-1332 doi: 10.1088/0256-307X/22/6/009
    [91]
    Li CG, Chen LN, Aihara K. Synchronization of coupled nonidentical genetic oscillators. Physical Biology, 2006, 3(1):33-37 https://www.researchgate.net/publication/7198068_Synchronization_of_Coupled_Nonidentical_Genetic_Oscillators
    [92]
    Huang H, Feng G. Synchronization of nonidentical chaotic neural networks with time delays. Neural Networks, 2009, 22(7):869-874 doi: 10.1016/j.neunet.2009.06.009
    [93]
    Song YL, Tadé MO. Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling. Nonlinearity, 2009, 22(5):975-1001 doi: 10.1088/0951-7715/22/5/004
    [94]
    Song YL, Makarov VA, Velarde MG. Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks. Biological Cybernatics, 2009, 101(2):147-167 doi: 10.1007/s00422-009-0326-5
    [95]
    Tass PA. Phase Resetting in Medicine and Biology:Stochastic Modeling and Data Analysis. Berlin:Springer, 1999
    [96]
    Tass PA. A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biological Cybernetics, 2003, 89(2):81-88 doi: 10.1007/s00422-003-0425-7
    [97]
    Tukhlina N, Rosenblum M. Feedback suppression of neural synchrony in two interacting populations by vanishing stimulation. Journal of Biological Physics, 2008, 34(3):301-314 doi: 10.1007/s10867-008-9081-4
    [98]
    Luo M, Xu J. Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators. Biological Cybernetics, 2009, 101(3):241-246 doi: 10.1007/s00422-009-0334-5
    [99]
    Strogatz SH, Abrams DM, Mcrobie A, et al. Crowd synchrony on the Millennium Bridge. Nature, 2005, 438(7064):43-44 doi: 10.1038/438043a
    [100]
    Eckhardt B, Ott E, Strogatz SH, et al. Modeling walker synchronization on the Millennium Bridge. Physical Review E, 2007, 75:021110 doi: 10.1103/PhysRevE.75.021110
    [101]
    Wong KW, Zhen B, Xu J et al. An analytic criterion for generalized synchronization in unidirectionally coupled systems based on the auxiliary system approach. Chaos, 2012, 22:033146 doi: 10.1063/1.4748862
    [102]
    Wang L, Zhen B, Xu J. A simple approach to achieve modified projective synchronization between two different chaotic systems. The Scientific World Journal, 2013, 2013:568194 https://www.researchgate.net/publication/258254976_A_Simple_Approach_to_Achieve_Modified_Projective_Synchronization_between_Two_Different_Chaotic_Systems
    [103]
    Song YL, Xu J. Inphase and antiphase synchronization in a delaycoupled system with applications to a delay-coipled FitzHughNagumo system. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(10):1659-1670 doi: 10.1109/TNNLS.2012.2209459
    [104]
    Song YL. Hopf bifurcation and spatio-temporal patterns in delaycoupled van der Pol oscillators. Nonlinear dynamics, 2011, 63(1-2):223-237 doi: 10.1007/s11071-010-9799-y
    [105]
    Song YL, Xu J, Zhang TH. Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling. Chaos, 2011, 21:023111 doi: 10.1063/1.3578046
    [106]
    Ge JH, Xu J. Synchronization and synchronized periodic solution in a simplified five-neuron BAM neural network with delays. Neuro-computing, 2011, 74(6):993-999 http://www.sciencedirect.com/science/article/pii/S0925231210004790
    [107]
    Sun XT, Xu J. Delay induced resonances in a system of coherent interaction of lasers. Journal of Vibration Engineering and Technology, 2014, 2(2):141-15650 Li Q, Zhu Y, Xu D, et al. A negative stiffness vibration isol
    [108]
    Wang L, Zhao HY. Synchronized stability in a reaction-diffusion neural network model. Physics Letters A, 2014, 378(48):3586-3599 doi: 10.1016/j.physleta.2014.10.019
    [109]
    Luo M, Xu J. Suppression of collective synchronization in system of neural groups with washout-filter aided feedback. Neural Networks, 2011, 24(6):538-543 doi: 10.1016/j.neunet.2011.02.008
    [110]
    邓杨, 彭志科, 杨扬等.基于参数化时频分析的非线性振动系统参数辨识.力学学报, 2013, 45(6):992-996 doi: 10.6052/0459-1879-13-125

    De Yang, Peng Zhike, Yang Yang, et al. Identification of nonlinear vibration systems based on parametric TFA. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6):992-996 (in Chinese) doi: 10.6052/0459-1879-13-125
    [111]
    谢永, 刘盼, 蔡国平.基于加速度信号的柔性板的挠性参数辨识.力学学报, 2014, 46(1):128-135 doi: 10.6052/0459-1879-13-124

    Xie Yong, Liu Pan, Cai Guoping. Parameter identification of flexible plate based on the acceleration output. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1):128-135 (in Chinese) doi: 10.6052/0459-1879-13-124
    [112]
    Xu Q, Wang ZH. Exact stability test of neural delay differential equations via a rough estimation of the testing integral. International Journal of Dynamics and Control, 2014, 2(2):154-163 doi: 10.1007/s40435-013-0044-7
    [113]
    Xu Q, Stepan G, Wang ZH. Delay-dependent stability analysis by using delay-independent integral evaluation. Automatica, 2016, 70: 153-157 doi: 10.1016/j.automatica.2016.03.028
    [114]
    Xu Q, Stepan Gabor, Wang ZH. Balancing a wheeled inverted pendulum with a single accelerometer in the presence of time delay. Journal of Vibration and Control, 2017, 23(4):604-614 doi: 10.1177/1077546315583400
    [115]
    He YQ, Han JD. Acceleration-feedback-enhanced robust control of an unmanned helicopter. Journal of Guidance, Control and Dynamics, 2010, 33(4):1236-1250 doi: 10.2514/1.45659
    [116]
    Wang ZH, Hu HY, Xu Q, et al. Effect of delay combinations on stability and Hopf bifurcation of an oscillator with accelerationderivative feedback. International Journal of Nonlinear Mechanics, doi:10.1016/j.ijnonlinmec.2016.10.008
    [117]
    高雪, 陈前, 刘先斌.一类分段光滑隔振系统的非线性动力学设计方法.力学学报, 2016, 48(1):192-200 doi: 10.6052/0459-1879-15-099

    Gao Xue, Chen Qian, Liu Xianbin. Nonlinear dynamics design for piecewise smooth vibration isolation system. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1):192-200 (in Chinese) doi: 10.6052/0459-1879-15-099
    [118]
    王在华, 胡海岩.具有采样反馈的力控制系统稳定性.力学学报, 2016, 48(6):1372-1381 http://lxxb.cstam.org.cn/CN/abstract/abstract146108.shtml

    Wang Zaihua, Hu Haiyan. Stability of a force control system with sampled-data feedback. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6):1372-1381 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract146108.shtml
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