[1] BATTISTON, F., NICOSIA, V., and LATORA, V. Structural measures for multiplex networks. Physical Review E, 89, 032804(2014)
[2] BOCCALETTI, S., BIANCONI, G., CRIADO, R., DEL GENIO, C. I., GOMEZ-GARDENES, J., ROMANCE, M., SENDINA-NADAL, I., WANG, Z., and ZANIN, M. The structure and dynamics of multilayer networks. Physics Reports, 544, 1-122(2014)
[3] GOMEZ, S., DIAZ-GUILERA, A., GOMEZ-GARDENES, PEREZ-VICENTE, C. J., MORENO, Y., and ARENAS, A. Diffusion dynamics on multiplex networks. Physical Review Letters, 110, 028701(2013)
[4] ZHOU, C. S., ZEMANOVA, L., ZAMORA-LOPEZ, G., HILGETAG, C. C., and KURTHS, J. Structure-function relationship in complex brain networks expressed by hierarchical synchronization. New Journal of Physics, 9, 178(2007)
[5] SUN, W. G., WANG, R. B., WANG, W. X., and CAO, J. T. Analyzing inner and outer synchronization between two coupled discrete-time networks with time delays. Cognitive Neurodynamics, 4, 225-231(2010)
[6] BENTLEY, B., BRANICKY, R., BARNES, C. L., CHEW, Y. L., YEMINI, E., BULLMORE, E. T., VERTES, P. E., and SCHAFER, W. R. The multilayer connectome of Caenorhabditis elegans. PLoS Computational Biology, 12, e1005283(2016)
[7] NIKITIN, D., OMELCHENKO, I., ZAKHAROVA, A., AVETYAN, M., FRADKOV, A. L., and SCHOLL, E. Complex partial synchronization patterns in networks of delay-coupled neurons. Philosophical Transactions of the Royal Society A, 377, 20180128(2019)
[8] CARDILLO, A., ZANIN, M., GOMEZ-GARDENES, ROMANCE, M., GARCIA DEL AMO, A. J., and BOCCALETTI, S. Modeling the multi-layer nature of the European Air Transport Network: resilience and passengers re-scheduling under random failures. European Physical JournalSpecial Topics, 215, 23-33(2013)
[9] BATTISTON, F., NICOSIA, V., CHAVEZ, M., and LATORA, V. Multilayer motif analysis of brain networks. Chaos, 27, 047404(2017)
[10] KORN, H. and FAURE, P. Is there chaos in the brain? II. experimental evidence and related models. Comptes Rendus Biologies, 326, 787-840(2003)
[11] HU, X. Y., LIU, C. X., LIU, L., NI, J. K., and YAO, Y. P. Chaotic dynamics in a neural network under electromagnetic radiation. Nonlinear Dynamics, 91, 1541-1554(2018)
[12] ZHOU, L. L., TAN, F., YU, F., and LIU, W. Cluster synchronization of two-layer nonlinearly coupled multiplex networks with multi-links and time-delays. Neurocomputing, 359, 264-275(2019)
[13] MAJHI, S., PERC, M., and GHOSH, D. Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos, 27, 073109(2017)
[14] YU, Y. and WANG, Q. Y. Oscillation dynamics in an extended model of thalamic-basal ganglia. Nonlinear Dynamics, 98, 1065-1080(2019)
[15] MA, J., YANG, Z. Q., YANG, L. J., and TANG, J. A physical view of computational neurodynamics. Journal of Zhejiang University-Science A, 20, 639-659(2019)
[16] ZHOU, J., LIU, Z. R., and XIANG, L. Global dynamics of delayed bidirectional associative memory (BAM) neural networks. Applied Mathematics and Mechanics (English Edition), 26(3), 327-335(2005) https://doi.org/10.1007/BF02440083
[17] KACHHVAH, A. D. and JALAN, S. Delay regulated explosive synchronization in multiplex networks. New Journal of Physics, 21, 015006(2019)
[18] SAWICKI, J., OMELCHENKO, I., ZAKHAROVA, A., and SCHOELL, E. Delay controls chimera relay synchronization in multiplex networks. Physical Review E, 98, 062224(2018)
[19] HAMMOND, C., BERGMAN, H., and BROWN, P. Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends in Neurosciences, 30, 357-364(2007)
[20] MAO, X. C. and WANG, Z. H. Stability, bifurcation, and synchronization of delay-coupled ring neural networks. Nonlinear Dynamics, 84, 1063-1078(2016)
[21] TANG, Y., QIAN, F., GAO, H. J., and KURTHS, J. Synchronization in complex networks and its application — a survey of recent advances and challenges. Annual Reviews in Control, 38, 184-198(2014)
[22] HAN, F., GU, X. C., WANG, Z. J., FAN, H., CAO, J. F., and LU, Q. S. Global firing rate contrast enhancement in E/I neuronal networks by recurrent synchronized inhibition. Chaos, 28, 106324(2018)
[23] FAN, D. G., ZHENG, Y. H., YANG, Z. C., and WANG, Q. Y. Improving control effects of absence seizures using single-pulse alternately resetting stimulation (SARS) of corticothalamic circuit. Applied Mathematics and Mechanics (English Edition), 41(9), 1287-1302(2020) https://doi.org/10.1007/s10483-020-2644-8
[24] LIANG, S. and WANG, Z. H. Controlling a neuron by stimulating a coupled neuron. Applied Mathematics and Mechanics (English Edition), 40(1), 13-24(2019) https://doi.org/10.1007/s10483- 019-2407-8
[25] HU, H. Y. and WANG, Z. H. Dynamics of Controlled Mechanical Systems with Delayed Feedback, Springer-Verlag, Heidelberg (2002)
[26] CHEN, L. X. and CAI, G. P. Design method of multiple time-delay controller for active structural vibration control. Applied Mathematics and Mechanics (English Edition), 30(11), 1405-1414(2009) https://doi.org/10.1007/s10483-009-1106-z
[27] STEPAN, G. Delay effects in brain dynamics. Philosophical Transactions of the Royal Society A, 367, 1059-1062(2009)
[28] FLUNKERT, V., FISCHER, I., and SCHOELL, E. Dynamics, control and information in delaycoupled systems. Philosophical Transactions of the Royal Society A, 371, 20120465(2013)
[29] WANG, Y. P., CONG, Y. H., and HU, G. D. Delay-dependent stability of linear multistep methods for differential systems with distributed delays. Applied Mathematics and Mechanics (English Edition), 39(12), 1837-1844(2018) https://doi.org/10.1007/s10483-018-2392-9
[30] BALDI, P. and ATIYA, A. F. How delays affect neural dynamics and learning. IEEE Transactions on Neural Networks, 5, 612-621(1994)
[31] MAO, X. C., SUN, J. Q., and LI, S. F. Dynamics of delay-coupled FitzHugh-Nagumo neural rings. Chaos, 28, 013104(2018)
[32] CAMPBELL, S. A., EDWARDS, R., and VAN DEN DRIESSCHE, P. Delayed coupling between two neural network loops. SIAM Journal on Applied Mathematics, 65, 316-335(2005)
[33] HSU, C. H. and YANG, T. S. Periodic oscillations arising and death in delay-coupled neural loops. International Journal of Bifurcation and Chaos, 17, 4015-4032(2007)
[34] MAO, X. C., ZHOU, X. Y., SHI, T. T., and QIAO, L. Dynamical analysis of coupled bidirectional FitzHugh-Nagumo neuronal networks with multiple delays. Journal of Computational and Nonlinear Dynamics, 14, 061002(2019)
[35] SINGH, A., GHOSH, S., JALAN, S., and KURTHS, J. Synchronization in delayed multiplex networks. Europhysics Letters, 111, 30010(2015)
[36] CHENG, C. Y. Induction of Hopf bifurcation and oscillation death by delays in coupled networks. Physics Letters A, 374, 178-185(2009)
[37] SONG, Y. L. and XU, J. Inphase and antiphase synchronization in a delay-coupled system with applications to a delay-coupled FitzHugh-Nagumo system. IEEE Transactions on Neural Networks and Learning Systems, 23, 1659-1670(2012)
[38] XU, X., YU, D., and WANG, Z. Inter-layer synchronization of periodic solutions in two coupled rings with time delay. Physica D, 396, 1-11(2019)
[39] HOPFIELD, J. J. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences of the United States of American, 81, 3088-3092(1984)
[40] HASSARD, B. D., KAZARINOFF, N. D., and WAN, Y. H. Theory and Application of Hopf Bifurcation, Cambridge University Press, Cambridge (1981)
[41] DUAN, S. K. and LIAO, X. F. An electronic implementation for Liao’s chaotic delayed neuron model with non-monotonous activation function. Physics Letters A, 369, 37-43(2007)
[42] BAO, B. C., QIAN, H., XU, Q., CHEN, M., WANG, J., and YU, Y. J. Coexisting behaviors of asymmetric attractors in hyperbolic-type memristor based Hopfield neural network. Frontiers in Computational Neuroscience, 11, 81(2017)
[43] ABLAY, G. Novel chaotic delay systems and electronic circuit solutions. Nonlinear Dynamics, 81, 1795-1804(2015)