Effects of frustration on explosive synchronization

doi:10.1007/s11467-016-0597-y

Front. Phys.

2016, Vol. 11

Issue (6) : 110504 https://doi.org/10.1007/s11467-016-0597-y

Research article

Effects of frustration on explosive synchronization

Xia Huang¹,Jian Gao²,Yu-Ting Sun²,Zhi-Gang Zheng³,Can Xu^2,^*(

)

¹. Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
². Department of Physics and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China
³. College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China

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Abstract

In this study, we consider the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and frustration is included in the system. This assumption can enhance or delay the explosive transition to synchronization. Interestingly, a de-synchronization phenomenon occurs and the type of phase transition is also changed. Furthermore, we provide an analytical treatment based on a star graph, which resembles that obtained in scale-free networks. Finally, a self-consistent approach is implemented to study the de-synchronization regime. Our findings have important implications for controlling synchronization in complex networks because frustration is a controllable parameter in experiments and a discontinuous abrupt phase transition is always dangerous in engineering in the real world.

Keywords coupled phase oscillator explosive synchronization frustration

Corresponding Author(s): Can Xu

Issue Date: 06 June 2016

Cite this article:

Xia Huang,Jian Gao,Yu-Ting Sun, et al. Effects of frustration on explosive synchronization[J]. Front. Phys. , 2016, 11(6): 110504.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-016-0597-y
https://academic.hep.com.cn/fop/EN/Y2016/V11/I6/110504

1	A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge: Cambridge University Press, 2001, pp 279–296 https://doi.org/10.1017/CBO9780511755743.013
2	J. Buck, Synchronous rhythmic flashing of fireflies (II), Q. Rev. Biol. 63(3), 265 (1988) https://doi.org/10.1086/415929
3	B. Georges, J. Grollier, V. Cros, and A. Fert, Impact of the electrical connection of spin transfer nano-oscillators on their synchronization: An analytical study, Appl. Phys. Lett. 92(23), 232504 (2008) https://doi.org/10.1063/1.2945636
4	I. Z. Kiss, Y. Zhai, and J. L. Hudson, Emerging coherence in a population of chemical oscillators, Science 296(5573), 1676 (2002) https://doi.org/10.1126/science.1070757
5	B. Eckhardt, E. Ott, S. H. Strogatz, D. M. Abrams, and A. McRobie, Modeling walker synchronization on the Millennium Bridge, Phys. Rev. E 75(2), 021110 (2007) https://doi.org/10.1103/PhysRevE.75.021110
6	Z. Néda, E. Ravasz, T. Vicsek, Y. Brechet, and A. L. Barabási, Physics of the rhythmic applause, Phys. Rev. E 61, 6987 (2000) https://doi.org/10.1103/PhysRevE.61.6987
7	Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Berlin: Springer, 1984, pp 75–76 https://doi.org/10.1007/978-3-642-69689-3
8	S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D 143(1–4), 1 (2000) https://doi.org/10.1016/S0167-2789(00)00094-4
9	J. A. Acebrón, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77(1), 137 (2005) https://doi.org/10.1103/RevModPhys.77.137
10	A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Phys. Rep. 469(3), 93 (2008) https://doi.org/10.1016/j.physrep.2008.09.002
11	F. A. Rodrigues, T. K. D. M. Peron, P. Ji, and J. Kurths, The Kuramoto model in complex networks, Phys. Rep. 610, 1 (2016) https://doi.org/10.1016/j.physrep.2015.10.008
12	J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scalefree networks, Phys. Rev. Lett. 106(12), 128701 (2011) https://doi.org/10.1103/PhysRevLett.106.128701
13	W. Q. Liu, Y. Wu, J. H. Xiao, and M. Zhan, Effects of frequency-degree correlation on synchronization transition in scale-free networks, Europhys. Lett. 101(3), 38002 (2013) https://doi.org/10.1209/0295-5075/101/38002
14	T. K. D. M. Peron and F. A. Rodrigues, Explosive synchronization enhanced by time-delayed coupling, Phys. Rev. E 86(1), 016102 (2012) https://doi.org/10.1103/PhysRevE.86.016102
15	I. Leyva, A. Navas, I. Sendina-Nadal, J. A. Almendral, J. M. Buldú, M. Zanin, D. Papo, and S. Boccaletti, Explosive transitions to synchronization in networks of phase oscillators, Sci. Rep. 3, 1281 (2013) https://doi.org/10.1038/srep01281
16	L. H. Zhu, L. Tian, and D. N. Shi, Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators, Phys. Rev. E 88(4), 042921 (2013) https://doi.org/10.1103/PhysRevE.88.042921
17	X. Zhang, X. Hu, J. Kurths, and Z. Liu, Explosive synchronization in a general complex network, Phys. Rev. E 88, 010802(R) (2013)
18	I. Leyva, I. Sendina-Nadal, J. A. Almendral, A. Navas, S. Olmi, and S. Boccaletti, Explosive synchronization in weighted complex networks, Phys. Rev. E 88(4), 042808 (2013) https://doi.org/10.1103/PhysRevE.88.042808
19	X. Hu, S. Boccaletti, W. Huang, X. Zhang, Z. Liu, S. Guan, and C. H. Lai, Exact solution for first-order synchronization transition in a generalized Kuramoto model, Sci. Rep. 4, 7262 (2014) https://doi.org/10.1038/srep07262
20	C. Xu, Y. Sun, J. Gao, T. Qiu, Z. Zheng, and S. Guan, Synchronization of phase oscillators with frequencyweighted coupling, Sci. Rep. 6, 21926 (2016) https://doi.org/10.1038/srep21926
21	P. Li, K. Zhang, X. Xu, J. Zhang, and M. Small, Reexamination of explosive synchronization in scale-free networks: The effect of disassortativity, Phys. Rev. E 87(4), 042803 (2013) https://doi.org/10.1103/PhysRevE.87.042803
22	I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendiña- Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, and S. Boccaletti, Explosive first-order transition to synchrony in networked chaotic oscillators, Phys. Rev. Lett. 108, 168702 (2012) https://doi.org/10.1103/PhysRevLett.108.168702
23	P. Ji, T. K. D. M. Peron, P. J. Menck, F. A. Rodrigues, and J. Kurths, Cluster Explosive Synchronization in Complex Networks, Phys. Rev. Lett. 110(21), 218701 (2013) https://doi.org/10.1103/PhysRevLett.110.218701
24	T. K. D. M. Peron and F. A. Rodrigues, Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations, Phys. Rev. E 86(5), 056108 (2012) https://doi.org/10.1103/PhysRevE.86.056108
25	B. C. Coutinho, A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Kuramoto model with frequency-degree correlations on complex networks, Phys. Rev. E 87(3), 032106 (2013) https://doi.org/10.1103/PhysRevE.87.032106
26	Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Basin of Attraction Determines Hysteresis in Explosive Synchronization, Phys. Rev. Lett. 112(11), 114102 (2014) https://doi.org/10.1103/PhysRevLett.112.114102
27	P. S. Skardal and A. Arenas, Disorder induces explosive synchronization, Phys. Rev. E 89(6), 062811 (2014) https://doi.org/10.1103/PhysRevE.89.062811
28	H. Bi, X. Hu, X. Zhang, Y. Zou, Z. Liu, and S. Guan, Explosive oscillation death in coupled Stuart-Landau oscillators, Europhys. Lett. 108(5), 50003 (2014) https://doi.org/10.1209/0295-5075/108/50003
29	Y. Chen, Z. Cao, S. Wang, and G. Hu, Self-organized correlations lead to explosive synchronization, Phys. Rev. E 92(2), 022810 (2015) https://doi.org/10.1103/PhysRevE.91.022810
30	P. Ji, T. K. D. Peron, F. A. Rodrigues, and J. Kurths, Analysis of cluster explosive synchronization in complex networks, Phys. Rev. E 90(6), 062810 (2014) https://doi.org/10.1103/PhysRevE.90.062810
31	X. Zhang, S. Boccaletti, S. Guan, and Z. Liu, Explosive Synchronization in Adaptive and Multilayer Networks, Phys. Rev. Lett. 114(3), 038701 (2015) https://doi.org/10.1103/PhysRevLett.114.038701
32	P. Ji, T. K. Peron, F. A. Rodrigues, and J. Kurths, Lowdimensional behavior of Kuramoto model with inertia in complex networks, Sci. Rep. 4, 4783 (2014) https://doi.org/10.1038/srep04783
33	X. Zhang, Y. Zou, S. Boccaletti, and Z. Liu, Explosive synchronization as a process of explosive percolation in dynamical phase space, Sci. Rep. 4, 5200 (2014) https://doi.org/10.1038/srep05200
34	R. S. Pinto and A. Saa, Explosive synchronization with partial degree-frequency correlation, Phys. Rev. E 91(2), 022818 (2015) https://doi.org/10.1103/PhysRevE.91.022818
35	S. Yoon, M. Sorbaro Sindaci, A. V. Goltsev, and J. F. F. Mendes, Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks, Phys. Rev. E 91(3), 032814 (2015) https://doi.org/10.1103/PhysRevE.91.032814
36	C. Xu, J. Gao, Y. Sun, X. Huang, and Z. Zheng, Explosive or continuous: Incoherent state determines the route to synchronization, Sci. Rep. 5, 12039 (2015) https://doi.org/10.1038/srep12039
37	S. Ma, H. Bi, Y. Zou, Z. Liu, and S. Guan, Shuttle-run synchronization in mobile ad hoc networks, Front. Phys. 10(3), 100505 (2015) https://doi.org/10.1007/s11467-015-0475-z
38	S. Liu, G. Zhang, Z. He, and M. Zhan, Optimal configuration for vibration frequencies in a ring of harmonic oscillators: The nonidentical mass effect, Front. Phys. 10(3), 100503 (2015) https://doi.org/10.1007/s11467-015-0462-4
39	Y. Zhang and W. Wan, States and transitions in mixed networks, Front. Phys. 9(4), 523 (2014) https://doi.org/10.1007/s11467-014-0426-0
40	X. Huang, M. Zhan, F. Li, and Z. Zheng, Singleclustering synchronization in a ring of Kuramoto oscillators, J. Phys. A Math. Theor. 47(12), 125101 (2014) https://doi.org/10.1088/1751-8113/47/12/125101
41	Z. G. Zheng, Frustration effect on synchronization and chaos in coupled oscillators, Chin. Phys. 10, 0703 (2001)
42	H. Sakaguchi, S. Shinmoto, and Y. kuramoto, Mutual entrainment in oscillator lattices with nonvariational type interaction, Prog. Theor. Phys. 79, 1096 (1988)
43	E. Berg, E. Altman, and A. Auerbach, Singlet excitations in pyrochlore: A study of quantum frustration, Phys. Rev. Lett. 90(14), 147204 (2003) https://doi.org/10.1103/PhysRevLett.90.147204
44	O. E. Omelćhenko and M. Wolfrum, Nonuniversal transitions to synchrony in the Sakaguchi–Kuramoto model, Phys. Rev. Lett. 109, 164101 (2012) https://doi.org/10.1103/PhysRevLett.109.164101
45	C. Yokoi, L. Tang, and W. Chou, Ground state of the one-dimensional chiral XY model in a field,Phys. Rev. B 37(4), 2173 (1988) https://doi.org/10.1103/PhysRevB.37.2173

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