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Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling |
| Yun Zhai(翟云)1,2,3, Jinghua Xiao(肖井华)1, and Zhigang Zheng(郑志刚)2,3,† |
1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China;
3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China |
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Abstract Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.
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Received: 09 February 2023
Revised: 22 February 2023
Accepted manuscript online: 02 March 2023
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PACS:
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05.45.Xt
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(Synchronization; coupled oscillators)
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05.45.Ra
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(Coupled map lattices)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11875135). |
Corresponding Authors:
Zhigang Zheng
E-mail: zgzheng@bnu.edu.cn
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Cite this article:
Yun Zhai(翟云), Jinghua Xiao(肖井华), and Zhigang Zheng(郑志刚) Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling 2023 Chin. Phys. B 32 060505
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[1] Auyang S Y1998 Foundations of complex-system theories: In economics, evolutionary biology, and statistical physics (Cambridge: Cambridge University Press)
[2] Zheng Z G2021 An introduction to emergence dynamics in complex systems (Singapore: Springer Singapore) pp. 133-196
[3] Pikovsky A, Rosenblum M and Kurths J2001 Synchronization: a universal concept in nonlinear sciences (Cambridge: Cambridge University Press)
[4] Osaka M2017 Appl. Math. B 8 1227
[5] Jia J, Song Z W, Liu W Q, Kurths J and Xiao J2015 Sci. Rep. 5 e0118986
[6] Ermentrout B1991 J. Math. Biol. 29 571
[7] Buck J B and Buck E1968 Science 159 1319
[8] Kiss I Z, Zhai Y and Hudson J L2002 Science 296 1676
[9] Pantaleone J1998 Phys. Rev. D 58 073002
[10] Witthaut D, Hellmann F, Kurths J, Kettemann S, Meyer-Ortmanns H and Timme M2022 Rev. Mod. Phys. 94 015005
[11] Bick C, Goodfellow M, Laing C R and Martens E A2020 J. Math. Neurosci. 10 9
[12] Pecora L M and Carroll T L1990 Phys. Rev. Lett. 64 821
[13] Yang J Z, Hu G and Xiao J H1998 Phys. Rev. Lett. 80 496
[14] Rulkov N F, Sushchik M M, Tsimring L S and Abarbanel H D I1995 Phys. Rev. E 51 980
[15] Zheng Z G and Hu G2000 Phys. Rev. E 62 7882
[16] Rosenblum M G, Pikovsky A S and Kurths J1997 Phys. Rev. Lett. 78 4193
[17] Hampton A and Zanette D H1999 Phys. Rev. Lett. 83 2179
[18] Albert R and Barabasi A -L2002 Rev. Mod. Phys. 74 47
[19] Dorogovtsev S N and Mendes J F F2022 The nature of complex networks (OUP Oxford)
[20] Wang X F2002 Int. J. Bifurc. Chaos 12 885
[21] Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U2006 Phys. Rep. 424 175
[22] Arenas A, Daz-Guilera A, Kurths J, Moreno Y and Zhou C2008 Phys. Rep. 469 93
[23] Boccaletti S, Almendral J A, Guan S, Leyva I, Liu Z, Sendiña-Nadal I, Wang Z and Zou Y2016 Phys. Rep. 660 1
[24] Winfree A T1967 J. Theor. Biol. 16 15
[25] Kuramoto Y1975 in International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki (Berlin, Heidelberg: Springer Berlin Heidelberg) pp. 420-422
[26] Acebron J A, Bonilla L L, Perez Vicente C J, Ritort F and Spigler R2005 Rev. Mod. Phys. 77 137
[27] Rodrigues F A, Peron T K D M, Ji P and Kurths J2016 Phys. Rep. 610 1
[28] Kaneko K1991 Physica D 54 5
[29] Jensen M H, Bak P and Bohr T1983 Phys. Rev. Lett. 50 1637
[30] Grebogi C, Ott E and Yorke J A1983 Phys. Rev. Lett. 51 339
[31] Grebogi C, Ott E and Yorke J A1985 Physica D 15 354
[32] Bauer M and Martienssen W1991 Network: Computation In Neural Systems 2 345
[33] Chatterjee and Gupte1996 Phys. Rev. E 53 4457
[34] Qin W X2001 Int. J. Bifurc. Chaos 11 2245
[35] Osipov G V and Kurths J2002 Phys. Rev. E 65 016216
[36] Janaki T M, Sinha S and Gupte N2003 Phys. Rev. E 67 056218
[37] Woo S J, Lee J and Lee K J2003 Phys. Rev. E 68 016208
[38] Sonawane A R2010 Phys. Rev. E 81 056206
[39] Das A and Gupte N2013 Phys. Rev. E 87 042906
[40] Yamagishi J F and Kaneko K2020 Phys. Rev. Res. 2 023044
[41] Sélley F M and Tanzi M2021 J. Stat. Phys. 189 05618
[42] Kuramoto Y1984 Prog. Theor. Phys. 71 1182
[43] Ott E and Antonsen T M2008 Chaos 18 037113
[44] Ott E and Antonsen T M2009 Chaos 19 023117
[45] Watanabe S and Strogatz S H1993 Phys. Rev. Lett. 70 2391
[46] Watanabe S and Strogatz S H1994 Physica D 74 197
[47] Marvel S A, Mirollo R and Strogatz S H2009 Chaos 19 043104
[48] Zheng Z G, Hu G, and Hu B B1998 Phys. Rev. Lett. 81 5318
[49] Zheng Z G, Hu B B, and Hu G2000 Phys. Rev. E 62 402
[50] Hu B B and Zheng Z G2000 Int. J. Bifurc. Chaos 10 2399
[51] Zheng Z G2002 Commun. Theor. Phys. 37 557
[52] Xu C, Gao J, Xiang H R, Jia W J, Guan S G and Zheng Z G2016 Phys. Rev. E 94 062204
[53] Xu C, Sun Y T, Gao J, Qiu T, Zheng Z G and Guan S G2016 Sci. Rep. 6 21926
[54] Xu C, Boccaletti S, Guan S G and Zheng Z G2018 Phys. Rev. E 98 050202
[55] Cai Z K, Zheng Z G and Xu C2022 Commun. Nonlinear Sci. Numer. Simul. 107 106129
[56] Xu C, Xiang H R, Gao J and Zheng Z G2016 Sci. Rep. 6 31133
[57] Wang X, Zheng Z G and Xu C2021 Phys. Rev. E 104 054208
[58] Abrams D M and Strogatz S H2004 Phys. Rev. Lett. 93 174102
[59] Gómez-Gardeñes J, Gómez S, Arenas A and Moreno Y2011 Phys. Rev. Lett. 106 128701 |
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