States and transitions in mixed networks

doi:10.1007/s11467-014-0426-0

Front. Phys.

2014, Vol. 9

Issue (4) : 523-528 https://doi.org/10.1007/s11467-014-0426-0

RESEARCH ARTICLE

States and transitions in mixed networks

Ying Zhang¹,Wen-Hui Wan^2,^*(

)

1. Department of Physics, Beijing Normal University, Beijing 100875, China
2. Department of Physics, Beijing Institute of Technology, Beijing 100081, China

Download: PDF(490 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

A network is named as mixed network if it is composed of N nodes, the dynamics of some nodes are periodic, while the others are chaotic. The mixed network with all-to-all coupling and its corresponding networks after the nonlinearity gap-condition pruning are investigated. Several synchronization states are demonstrated in both systems, and a first-order phase transition is proposed. The mixture of dynamics implies any kind of synchronous dynamics for the whole network, and the mixed networks may be controlled by the nonlinearity gap-condition pruning.

Keywords mixed network phase transition synchronization state

Corresponding Author(s): Wen-Hui Wan

Issue Date: 26 August 2014

Cite this article:

Ying Zhang,Wen-Hui Wan. States and transitions in mixed networks[J]. Front. Phys. , 2014, 9(4): 523-528.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-014-0426-0
https://academic.hep.com.cn/fop/EN/Y2014/V9/I4/523

1	D. J. Watts and S. H. Strogatz, Collective dynamics of “small-world” networks, Nature, 1998, 393(6684): 440 doi: 10.1038/30918
2	B. Blasius, A. Huppert, and L. Stone, Complex dynamics and phase synchronization in spatially extended ecological systems, Nature, 1999, 399(6734): 354 doi: 10.1038/20676
3	G. B. Ermentrout and D. Kleinfeld, Traveling electrical waves in cortex, Neuron, 2001, 29(1): 33 doi: 10.1016/S0896-6273(01)00178-7
4	S. H. Strogatz, Exploring complex networks, Nature, 2001, 410(6825): 268 doi: 10.1038/35065725
5	M. Barahona and L. M. Pecora, Synchronization in smallworld systems, Phys. Rev. Lett., 2002, 89(5): 054101 doi: 10.1103/PhysRevLett.89.054101
6	Y. Moreno and A. F. Pacheco, Synchronization of Kuramoto oscillators in scale-free networks, Europhys. Lett., 2004, 68(4): 603 doi: 10.1209/epl/i2004-10238-x
7	D. S. Lee, Synchronization transition in scale-free networks: Clusters of synchrony, Phys. Rev. E, 2005, 72(2): 026208 doi: 10.1103/PhysRevE.72.026208
8	S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. Hwang, Complex networks: Structure and dynamics, Phys. Rep., 2006, 424(4-5): 175 doi: 10.1016/j.physrep.2005.10.009
9	A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Phys. Rep., 2008, 469(3): 93 doi: 10.1016/j.physrep.2008.09.002
10	Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Berlin: Springer-Verlag, 1984 doi: 10.1007/978-3-642-69689-3
11	D. Pazo, Thermodynamic limit of the first-order phase transition in the Kuramoto model, Phys. Rev. E, 2005, 72(4): 046211 doi: 10.1103/PhysRevE.72.046211
12	M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 2003, 45(2): 167 doi: 10.1137/S003614450342480
13	S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Complex networks: Structure and dynamics, Phys. Rep., 2006, 424(4-5): 175 doi: 10.1016/j.physrep.2005.10.009
14	D. Achlioptas, R. M. D’Souza, and J. Spencer, Explosive percolation in random networks, Science, 2009, 323(5920): 1453 doi: 10.1126/science.1167782
15	Y. S. Cho, J. S. Kim, J. Park, B. Kahng, and D. Kim, Percolation transitions in scale-free networks under the achlioptas process, Phys. Rev. Lett., 2009, 103(13): 135702 doi: 10.1103/PhysRevLett.103.135702
16	F. Radicchi and S. Fortunato, Explosive percolation in scalefree networks, Phys. Rev. Lett., 2009, 103(16): 168701 doi: 10.1103/PhysRevLett.103.168701
17	J. Gómez-Garde?es, S. Gómez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scale-free networks., Phys. Rev. Lett., 2011, 106(12): 128701 doi: 10.1103/PhysRevLett.106.128701
18	I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendi?a-Nadal, J. Gómez-Garde?es, 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., 2012, 108(16): 168702 doi: 10.1103/PhysRevLett.108.168702
19	I. Leyva, A. Navas, I. Sendi?a-Nadal, J. A. Almendral, J. M. Buldú, M. Zanin, D. Papo, and S. Boccaletti, Explosive transitions to synchronization in networks of phase oscillators, Scientific Reports, 2013, 3: 1281 doi: 10.1038/srep01281
20	Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Basin of attraction determines hysteresis in explosive synchronization, Phys. Rev. Lett., 2014, 112(11): 114102 doi: 10.1103/PhysRevLett.112.114102
21	R. M. May, Simple mathematical models with very complicated dynamics, Nature, 1976, 261(5560): 459 doi: 10.1038/261459a0
22	A. Hastings, C. Hom, S. Ellner, P. Turchin, and H. Godfray, Chaos in ecology: is mother nature a strange attractor? Annu. Rev. Ecol. Syst., 1993, 24: 1
23	B. E. Kendall and G. A. Fox, Spatial structure, environmental heterogeneity, and population dynamics: Analysis of the coupled logistic map, Theor. Popul. Biol., 1998, 54(1): 11 doi: 10.1006/tpbi.1998.1365
24	J. R. Groff, Exploring dynamical systems and chaos using the logistic map model of population change, Am. J. Phys., 2013, 81(10): 725 doi: 10.1119/1.4813114
25	J. Almeida, D. Peralta-Salas, and M. Romera, Can two chaotic systems give rise to order? Physica D, 2005, 200(1-2): 124 doi: 10.1016/j.physd.2004.10.003
26	E. Levinsohn, S. Mendoza, and E. Peacock-Lopez, Switching induced complex dynamics in an extended logistic map, Chaos Solitons Fractals, 2012, 45(4): 426 doi: 10.1016/j.chaos.2011.12.020

[1]	Zhen-Ming Xu (许震明). Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space[J]. Front. Phys. , 2021, 16(2): 24502-.
[2]	Jorge A. López, Claudio O. Dorso, Guillermo Frank. Properties of nuclear pastas[J]. Front. Phys. , 2021, 16(2): 24301-.
[3]	Shuang Zhou, Lu You, Hailin Zhou, Yong Pu, Zhigang Gui, Junling Wang. Van der Waals layered ferroelectric CuInP₂S₆: Physical properties and device applications[J]. Front. Phys. , 2021, 16(1): 13301-.
[4]	Lu Qi, Guo-Li Wang, Shutian Liu, Shou Zhang, Hong-Fu Wang. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice[J]. Front. Phys. , 2021, 16(1): 12503-.
[5]	Jin-Bo Wang, Rao Huang, Yu-Hua Wen. Thermally activated phase transitions in Fe-Ni core-shell nanoparticles[J]. Front. Phys. , 2019, 14(6): 63604-.
[6]	Yan-Rong Zhang, Ze-Zheng Zhang, Jia-Qi Yuan, Ming Kang, Jing Chen. High-order exceptional points in non-Hermitian Moiré lattices[J]. Front. Phys. , 2019, 14(5): 53603-.
[7]	Ai-Yuan Hu, Lin Wen, Guo-Pin Qin, Zhi-Min Wu, Peng Yu, Yu-Ting Cui. Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature[J]. Front. Phys. , 2019, 14(5): 53601-.
[8]	Gui-Lei Zhu, Xin-You Lü, Shang-Wu Bin, Cai You, Ying Wu. Entanglement and excited-state quantum phase transition in an extended Dicke model[J]. Front. Phys. , 2019, 14(5): 52602-.
[9]	Ai-Yuan Hu, Huai-Yu Wang. Phase transition of the frustrated antiferromagntic J₁-J₂-J₃ spin-1/2 Heisenberg model on a simple cubic lattice[J]. Front. Phys. , 2019, 14(1): 13605-.
[10]	Zhi Lin, Wanli Liu. Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices[J]. Front. Phys. , 2018, 13(5): 136402-.
[11]	Jian Lv, Xin Yang, Dan Xu, Yu-Xin Huang, Hong-Bo Wang, Hui Wang. High-pressure polymorphs of LiPN₂: A first-principles study[J]. Front. Phys. , 2018, 13(5): 136104-.
[12]	Xia Huang, Jin Dong, Wen-Jing Jia, Zhi-Gang Zheng, Can Xu. Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling[J]. Front. Phys. , 2018, 13(5): 130506-.
[13]	Kai-Tong Wang, Fuming Xu, Yanxia Xing, Hong-Kang Zhao. Evolution of individual quantum Hall edge states in the presence of disorder[J]. Front. Phys. , 2018, 13(4): 137306-.
[14]	Zhi Lin, Jun Zhang, Ying Jiang. Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method[J]. Front. Phys. , 2018, 13(4): 136401-.
[15]	Ning Liang, Fan Zhong. Renormalization group theory for temperature-driven first-order phase transitions in scalar models[J]. Front. Phys. , 2017, 12(6): 126403-.

Viewed

Full text

Abstract

Cited

Shared

Discussed