4 An Introduction to Emergence Dynamics in Complex Systems
195
72. Zheng, Z.G., Qian, Y.: Self-sustained oscillations in biological excitable media. Chin. Phys.
B 27(1), 018901 (2018)
73. Qian, Y., Zhang, G., Wang, Y.F., Yao, C.G., Zheng, Z.G.: Winfree loop sustained oscillation
in two-dimensional excitable lattices: Prediction and Realization. Chaos 29, 073106 (2019)
74. Qian, Y., Wang, Y., Zhang, G., Liu, F., Zheng, Z.G.: Collective sustained oscillations in
excitable small-world networks: the moderate fundamental loop or the minimum Winfree
loop? Nonlinear Dyn. 99(2), 1415 (2020)
75. Zhang, Z.Y., Zheng, Z.G., Niu, H.J., Mi, Y.Y., Wu, S., Hu, G.: Solving the inverse problem
of noise-driven dynamic networks. Phys. Rev. E 91, 012814 (2015)
76. Chen, Y., Wang, S.H., Zheng, Z.G., Zhang, Z.Y., Hu, G.: Depicting network structures from
variable data produced by unknown colored-noise driven dynamics. Europhys. Lett. 113,
18005 (2016)
77. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization, A Universal Concept in Nonlinear
Sciences. Cambridge University Press, New York (2001)
78. Strogatz, S.: Sync: The emerging science of spontaneous order, Hyperion, (2003)
79. Smith, H.M.: Synchronous flashing of fireflies. Science 82, 151 (1935)
80. Buck, J.B.: Synchronous rhythmic flashing of fireflies. Quart. Rev. Biol. 13(3), 301–314
(1938); Synchronous rhythmic flashing of fireflies. II. Quart. Rev. Biol. 63(3), 265–289 (1988)
81. Huygenii, G.: Horoloquim Oscilatorium Parisiis, France, (1673)
82. Winfree, A.T.: Biological rhythms and the behavior of populations of coupled oscillators. J.
Theo. Biol. 16, 15–42 (1967)
83. Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators. In:
International Symposium on Mathematical Problems in Theoretical Physics, Springer,
Berlin/Heidelberg, (1975), NBR 6023
84. Winfree, A.T.: Geometry of Biological Time. Springer-Verlag, New York (1990)
85. Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer-Verlag, Berlin (1984)
86. Acebrón, J.A., Bonilla, L.L., Vicente, C.J.P., Ritort, F., Spigler, R.: The Kuramoto model: A
simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77(1), 137 (2005)
87. Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex
networks. Phys. Rep. 469(3), 93–153 (2008)
88. Rodrigues, F.A., Peron, T.K.DM., Ji, P., Kurths, J.: The Kuramoto model in complex networks,
Phys. Rep. 610, 1–98 (2016)
89. Osipov, G.V., Kurths, J., Zhou, C.S.: Synchronization in Oscillatory Networks, Springer Series
in Synergetics, Springer-Verlag, Berlin, (2007)
90. Yao, N., Zheng, Z.G.: Chimera states in spatiotemporal systems: Theory and applications.
Int. J. Mod. Phys. B 30(7), 1630002 (2016)
91. Ott, E., Antonsen, T.M.: Low dimensional behavior of large systems of globally coupled
oscillators. Chaos 18(3), 037113 (2008)
92. Ott, E., Antonsen, T.M.: Long time evolution of phase oscillator systems. Chaos 19(2), 023117
(2009)
93. Marvel, S.A., Strogatz, S.H.: Invariant submanifold for series arrays of Josephson junctions.
Chaos 19(1), 013132 (2009)
94. Marvel, S.A., Mirollo, R.E., Strogatz, S.H.: Identical phase oscillators with global sinusoidal
coupling evolve by mobius group action. Chaos 19(4), 043104 (2009)
95. Hu, G., Xiao, J.H., Zheng, Z.G.: Chaos Control. Shanghai Sci. Tech. Edu. Pub. House,
Shanghai (2000)
96. Zheng, Z.G.: Collective Behaviors and Spatiotemporal Dynamics in Coupled Nonlinear
Systems. Higher Education Press, Beijing (2004)
97. Zheng, Z.G., Hu, G., Hu, B.: Phase slips and phase synchronization of coupled oscillators.
Phys. Rev. Lett. 81, 5318–5321 (1998)
98. Zheng, Z.G., Hu, B., Hu, G.: Collective phase slips and phase synchronizations in coupled
oscillator systems. Phys. Rev. E 62, 402–408 (2000)
99. Hu, B., Zheng, Z.G.: Phase synchronizations: transitions from high- to low-dimensional tori
through chaos. Inter. J. Bif. Chaos 10(10), 2399–2414 (2000)
195
72. Zheng, Z.G., Qian, Y.: Self-sustained oscillations in biological excitable media. Chin. Phys.
B 27(1), 018901 (2018)
73. Qian, Y., Zhang, G., Wang, Y.F., Yao, C.G., Zheng, Z.G.: Winfree loop sustained oscillation
in two-dimensional excitable lattices: Prediction and Realization. Chaos 29, 073106 (2019)
74. Qian, Y., Wang, Y., Zhang, G., Liu, F., Zheng, Z.G.: Collective sustained oscillations in
excitable small-world networks: the moderate fundamental loop or the minimum Winfree
loop? Nonlinear Dyn. 99(2), 1415 (2020)
75. Zhang, Z.Y., Zheng, Z.G., Niu, H.J., Mi, Y.Y., Wu, S., Hu, G.: Solving the inverse problem
of noise-driven dynamic networks. Phys. Rev. E 91, 012814 (2015)
76. Chen, Y., Wang, S.H., Zheng, Z.G., Zhang, Z.Y., Hu, G.: Depicting network structures from
variable data produced by unknown colored-noise driven dynamics. Europhys. Lett. 113,
18005 (2016)
77. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization, A Universal Concept in Nonlinear
Sciences. Cambridge University Press, New York (2001)
78. Strogatz, S.: Sync: The emerging science of spontaneous order, Hyperion, (2003)
79. Smith, H.M.: Synchronous flashing of fireflies. Science 82, 151 (1935)
80. Buck, J.B.: Synchronous rhythmic flashing of fireflies. Quart. Rev. Biol. 13(3), 301–314
(1938); Synchronous rhythmic flashing of fireflies. II. Quart. Rev. Biol. 63(3), 265–289 (1988)
81. Huygenii, G.: Horoloquim Oscilatorium Parisiis, France, (1673)
82. Winfree, A.T.: Biological rhythms and the behavior of populations of coupled oscillators. J.
Theo. Biol. 16, 15–42 (1967)
83. Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators. In:
International Symposium on Mathematical Problems in Theoretical Physics, Springer,
Berlin/Heidelberg, (1975), NBR 6023
84. Winfree, A.T.: Geometry of Biological Time. Springer-Verlag, New York (1990)
85. Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer-Verlag, Berlin (1984)
86. Acebrón, J.A., Bonilla, L.L., Vicente, C.J.P., Ritort, F., Spigler, R.: The Kuramoto model: A
simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77(1), 137 (2005)
87. Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex
networks. Phys. Rep. 469(3), 93–153 (2008)
88. Rodrigues, F.A., Peron, T.K.DM., Ji, P., Kurths, J.: The Kuramoto model in complex networks,
Phys. Rep. 610, 1–98 (2016)
89. Osipov, G.V., Kurths, J., Zhou, C.S.: Synchronization in Oscillatory Networks, Springer Series
in Synergetics, Springer-Verlag, Berlin, (2007)
90. Yao, N., Zheng, Z.G.: Chimera states in spatiotemporal systems: Theory and applications.
Int. J. Mod. Phys. B 30(7), 1630002 (2016)
91. Ott, E., Antonsen, T.M.: Low dimensional behavior of large systems of globally coupled
oscillators. Chaos 18(3), 037113 (2008)
92. Ott, E., Antonsen, T.M.: Long time evolution of phase oscillator systems. Chaos 19(2), 023117
(2009)
93. Marvel, S.A., Strogatz, S.H.: Invariant submanifold for series arrays of Josephson junctions.
Chaos 19(1), 013132 (2009)
94. Marvel, S.A., Mirollo, R.E., Strogatz, S.H.: Identical phase oscillators with global sinusoidal
coupling evolve by mobius group action. Chaos 19(4), 043104 (2009)
95. Hu, G., Xiao, J.H., Zheng, Z.G.: Chaos Control. Shanghai Sci. Tech. Edu. Pub. House,
Shanghai (2000)
96. Zheng, Z.G.: Collective Behaviors and Spatiotemporal Dynamics in Coupled Nonlinear
Systems. Higher Education Press, Beijing (2004)
97. Zheng, Z.G., Hu, G., Hu, B.: Phase slips and phase synchronization of coupled oscillators.
Phys. Rev. Lett. 81, 5318–5321 (1998)
98. Zheng, Z.G., Hu, B., Hu, G.: Collective phase slips and phase synchronizations in coupled
oscillator systems. Phys. Rev. E 62, 402–408 (2000)
99. Hu, B., Zheng, Z.G.: Phase synchronizations: transitions from high- to low-dimensional tori
through chaos. Inter. J. Bif. Chaos 10(10), 2399–2414 (2000)