Abstract
Various forms of oscillatory networks exist in our surrounding from neural cells to laser arrays. In many of these networks the nodes can go through a transient process of interaction and start oscillating in synchrony. Each of these nodes is characterized by its internal dynamics and changes its state accordingly. Using several forms of interactions, we numerically examine how the network dynamics is affected by network topology and potential random disturbances.
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References
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structure and dynamics. Phys. Rep. 424(4-5), 175–308 (2006)
Coutinho, B.C., Goltsev, A.V., Dorogovtsev, S.N., Mendes, J.F.F.: Kuramoto model with frequency-degree correlations on complex networks. Phys. Rev. EÂ 8(3), 32106 (2013)
Daido, H.: Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators. Prog. Theor. Phys. 88(6), 1213–1218 (1992)
Daido, H.: Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions. Phys. Rev. Lett. 68(7), 1073–1076 (1992)
Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)
Gómez-Gardeñes, J., Gómez, S., Arenas, A., Moreno, Y.: Explosive synchronization transitions in scale-free networks. Phys. Rev. Lett. 106(12), 128701 (2011)
Ichonmiya, T.: Frequency synchronization in a random oscillator network. Phys. Rev. EÂ 70(2), 26116 (2004)
Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Berlin (1984)
Mirchev, M.: Cooperative processes in complex networks with imperfections. Ph.D. thesis, Politecnico di Torino, Italy (2014)
Mirchev, M., Basnarkov, L., Corinto, F., Kocarev, L.: Cooperative phenomena in networks of oscillators with non-identical interactions and dynamics. IEEE Trans. Circuits Syst. I, Reg. Papers 61(3), 811–819 (2014)
Moreno, Y., Pacheco, A.F.: Synchronization of kuramoto oscillators in scale-free networks. Europhys. Lett. 68(4), 603–609 (2004)
Restrepo, J.G., Ott, E., Hunt, B.R.: Onset of synchronization in large networks of coupled oscillators. Phys. Rev. EÂ 71(3), 036151 (2005)
Sakaguchi, H., Kuramoto, Y.: A soluble active rotator model showing phase transitions via mutual entrainment. Prog. Theor. Phys. 76(3), 576–581 (1986)
Wiener, N.: Nonlinear Problems in Random Theory. MIT Press, Cambridge (1958)
Winfree, A.T.: Biological rhythms and the behavior of populations of coupled oscillators. J. Theor. Biol. 16(1), 15–42 (1967)
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Mirchev, M., Basnarkov, L., Kocarev, L. (2015). Cooperation among Non-identical Oscillators Connected in Different Topologies. In: Bogdanova, A., Gjorgjevikj, D. (eds) ICT Innovations 2014. ICT Innovations 2014. Advances in Intelligent Systems and Computing, vol 311. Springer, Cham. https://doi.org/10.1007/978-3-319-09879-1_27
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DOI: https://doi.org/10.1007/978-3-319-09879-1_27
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09878-4
Online ISBN: 978-3-319-09879-1
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