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Synchronization in Newman-Watts (NW) networks is studied in a Hindmarsh-Rose neuron dynamical system. The topological structures of some optimal synchronization networks are given. Numerical simulation results show that the synchronizability of the NW network is mainly determined by the distribution of coupling points in coupling space. The network with even distribution of coupling points generally has the strongest synchronizability. For a given number of edges there may exist some optimal synchronization networks with different topological structures. Optimal synchronization network has the strongest synchronizability, homogeneous degree distribution and better symmetry. However, its symmetry is not necessarily best. In general, optimal synchronization network is an irregular network. However, in the minor cases, the regular network may be an optimal synchronization network. A new type of network, the ergodic network, is introduced in this paper, and it has strong synchronizability as well as the characteristics of the optimal synchronization network.
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Keywords:
- Newman-Watts network /
- the degree of symmetry /
- coupling space /
- synchronization
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Hossein G N, Asad A, Morteza K 2013 Chin. Phys. B 22 070502
[3] Belousov B P 1958 Ref. Radiats. Med. 145
[4] Li X L, He J B, Lu D R, Wang H L 2002 Chin. J. Chin. Phys. 15 97 (in Chinese) [李学良, 何建波, 鲁道荣, 王华林 2002 化学 15 97]
[5] Zhang Z Z, Zeng S Y, Tang W Y, Hu J L, Zeng S W, Ning W L, Qiu Y, Wu H S 2012 Chin. Phys. B 21 108701
[6] Li J B, Lu Q C, Gong X W, Gong H Q, Zhang B M, Liang P J 2012 Acta Biophys. Sin. 28 119 (in Chinese) [李静波, 陆钦池, 宫新伟, 龚海庆, 张博明, 梁培基 2012 生物 28 119]
[7] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201 (in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 62 128201]
[8] Wu W S, Tang G N 2012 Acta Phys. Sin. 61 070505 (in Chinese) [吴望生, 唐国宁 2012 61 070505]
[9] Watts D J, Strogatz S H 1998 Nature 393 440
[10] Barabá si A L, Albert R 1999 Science 286 509
[11] Jost J, Joy M P 2001 Phys. Rev. E 65 016201
[12] Wang X F, Chen G 2002 Int. J. Bifurcation Chaos 12 187
[13] Barahona M, Pecora L M 2002 Phys. Rev. Lett. 89 054101
[14] Nishikawa T, Motter A E, Lai Y C, Hoppensteadt F C 2003 Phys. Rev. Lett. 91 014101
[15] Hong H, Kim B J, Choi M Y, Park H 2004 Phys. Rev. E 69 067105
[16] Cohen R, Havlin S 2003 Phys. Rev. Lett. 90 058701
[17] Motter A E, Zhou C, Kurths J 2005 Phys. Rev. Lett. 71 016116
[18] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[19] Zhao M, Zhou T, Wang B H, Yan G, Yang H J, Bai W J 2006 Physica A 371 773
[20] McGraw P N, Menzinger M 2005 Phys. Rev. E 72 015101
[21] Pecora L M, Carroll T L 1998 Phys. Rev. Lett. 80 2109
[22] Donetti L, Hurtado P I, Munoz M A 2005 Phys. Rev. Lett. 95 188701
[23] Nishikawa T, Motter A E 2006 Phys. Rev. E 73 065106
[24] Wang B, Tang H W, Xiu Z L, Guo C H 2006 Chin. Phys. Lett. 23 3123
[25] Estrada E, Gago S, Caporossi G 2010 Automatica 46 1835
[26] Newman M E J, Watts D J 1999 Phys. Lett. A 263 341
[27] Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Hossein G N, Asad A, Morteza K 2013 Chin. Phys. B 22 070502
[3] Belousov B P 1958 Ref. Radiats. Med. 145
[4] Li X L, He J B, Lu D R, Wang H L 2002 Chin. J. Chin. Phys. 15 97 (in Chinese) [李学良, 何建波, 鲁道荣, 王华林 2002 化学 15 97]
[5] Zhang Z Z, Zeng S Y, Tang W Y, Hu J L, Zeng S W, Ning W L, Qiu Y, Wu H S 2012 Chin. Phys. B 21 108701
[6] Li J B, Lu Q C, Gong X W, Gong H Q, Zhang B M, Liang P J 2012 Acta Biophys. Sin. 28 119 (in Chinese) [李静波, 陆钦池, 宫新伟, 龚海庆, 张博明, 梁培基 2012 生物 28 119]
[7] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201 (in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 62 128201]
[8] Wu W S, Tang G N 2012 Acta Phys. Sin. 61 070505 (in Chinese) [吴望生, 唐国宁 2012 61 070505]
[9] Watts D J, Strogatz S H 1998 Nature 393 440
[10] Barabá si A L, Albert R 1999 Science 286 509
[11] Jost J, Joy M P 2001 Phys. Rev. E 65 016201
[12] Wang X F, Chen G 2002 Int. J. Bifurcation Chaos 12 187
[13] Barahona M, Pecora L M 2002 Phys. Rev. Lett. 89 054101
[14] Nishikawa T, Motter A E, Lai Y C, Hoppensteadt F C 2003 Phys. Rev. Lett. 91 014101
[15] Hong H, Kim B J, Choi M Y, Park H 2004 Phys. Rev. E 69 067105
[16] Cohen R, Havlin S 2003 Phys. Rev. Lett. 90 058701
[17] Motter A E, Zhou C, Kurths J 2005 Phys. Rev. Lett. 71 016116
[18] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[19] Zhao M, Zhou T, Wang B H, Yan G, Yang H J, Bai W J 2006 Physica A 371 773
[20] McGraw P N, Menzinger M 2005 Phys. Rev. E 72 015101
[21] Pecora L M, Carroll T L 1998 Phys. Rev. Lett. 80 2109
[22] Donetti L, Hurtado P I, Munoz M A 2005 Phys. Rev. Lett. 95 188701
[23] Nishikawa T, Motter A E 2006 Phys. Rev. E 73 065106
[24] Wang B, Tang H W, Xiu Z L, Guo C H 2006 Chin. Phys. Lett. 23 3123
[25] Estrada E, Gago S, Caporossi G 2010 Automatica 46 1835
[26] Newman M E J, Watts D J 1999 Phys. Lett. A 263 341
[27] Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87
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