Improved functional-weight approach to oscillatory patterns in excitable networks
Tao Li(李涛)1,2, Lin Yan(严霖)1,2, and Zhigang Zheng(郑志刚)1,2,3,†
1 College of Information Science and Technology, Huaqiao University, Xiamen 361021, China; 2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China; 3 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
Abstract Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years. Although an individual unit is non-oscillatory, they may organize to form various collective oscillatory patterns through networked connections. An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions. The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network. In this paper, we develop the functional-weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics. This approach can be well applied to the study of sustained oscillations in coupled excitable units. We tested this scheme for different networks, such as homogeneous random networks, small-world networks, and scale-free networks and found it can accurately dig out the oscillation source and the propagation path. The present approach is believed to have the potential in studies competitive non-stationary dynamics.
Tao Li(李涛), Lin Yan(严霖), and Zhigang Zheng(郑志刚) Improved functional-weight approach to oscillatory patterns in excitable networks 2022 Chin. Phys. B 31 090502
[1] Watts D J and Strogatz S H 1998 Nature393 440 [2] Barabási A L and Albert R 1999 Science286 509 [3] Strogatz S H 2001 Nature410 268 [4] Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Phys. Rep.424 175 [5] Bullmore E and Sporns O 2009 Nat. Rev. Neurosci.10 186 [6] Glass L, Mackey M C and Zweifel P F 1989 Phys. Today42 72 [7] Goldbeter A and Keizer J 1998 Phys. Today51 86 [8] Tsai T Y C, Choi Y S, Ma W, Pomerening J R, Tang C and Ferrell J E Jr 2008 Science321 126 [9] Kuramoto Y 1975 International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics30 (New York:Springer) p. 420 [10] Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (Berlin:Springer) p. 111 [11] Kuramoto Y and Nishikawa I 1987 J. Stat. Phys.49 569 [12] Kuramoto Y 1991 Physica D50 15 [13] Winfree A T 1972 Science175 634 [14] Zhang Z K, Liu C, Zhan X X, Lu X, Zhang C X and Zhang Y C 2016 Phys. Rep.651 1 [15] Qian Y, Song X Y, Shi W, Chen G Z and Xue Y 2006 Acta Phys. Sin.55 4420 (in Chinese) [16] Ma J, Wang C N, Jin W Y, Li Y L and Pu Z S 2008 Chin. Phys. B17 2844 [17] Y Qian, X D Huang, X H Liao and G Hu 2010 Chin. Phys. B19 050513 [18] Ma X J, Huang L, Lai Y C and Zheng Z G 2009 Phys. Rev. E79 056106 [19] Ott E 1993 Chaos in Dynamical Systems. (Cambridge:Cambridge University Press) [20] O'Donovan M J 1999 Current Opinion in Neurobiology9 94 [21] Sanchez-Vives M V and McCormick D A 2000 Nature Neurosci.3 1027 [22] Lewis T J and Rinzel J 2000 Network:Comput. Neural Syst.11 299 [23] Karlebach G and Shamir R 2008 Nature Reviews Molecular Cell Biology9 770 [24] Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S J and Wu J Y 2004 J. Neurosci.24 9897 [25] Dahlem M A, Schneide F M and Schöll E 2008 Chaos18 026110 [26] Kanakov O I, Osipov G V, Chan C K and Kurths J 2007 Chaos17 015111 [27] Huang X D, Qian Y, Zhang X M and Hu G 2010 Phys. Rev. E81 051903 [28] Winfree A T 1991 Chaos1 303 [29] Qian Y, Huang X D, Hu G and Liao X H 2010 Phys. Rev. E81 036101 [30] Zhang Z Y, Li Z, Qian Y, Hu G and Zheng Z 2014 Europhys. Lett105 18003 [31] Zhang Z, Zheng Z, Niu H, Mi Y, Wu S and Hu G 2015 Phys. Rev. E91 012814 [32] Bär M and Eiswirth M 1993 Phys. Rev. E48 R1635 [33] Lewis T J and Rinzel J 2000 Network:Comput. Neural Syst.11 299 [34] Roxin A, Riecke H and Solla S A 2004 Phys. Rev. Lett.92 198101 [35] Müler-Linow M, Hilgetag C C and Hütt M T 2008 PLos Comput. Biol.4 e1000190 [36] Kuperman M and Abramson G 2001 Phys.Rev. Lett.86 2909 [37] Greenberg J M and Hastings S P 1978 SIAM J. Appl. Math.34 515 [38] Bak P, Chen K and Tang C 1990 Phys. Lett. A147 297 [39] Qian Y, Zhang C, Zhang G, Liu F and Zheng Z 2020 Nonlinear Dynamics99 1415
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
