×

Analysis and observation of moving domain fronts in a ring of coupled electronic self-oscillators. (English) Zbl 1390.34130

Summary: In this work, we consider a ring of coupled electronic (Wien-bridge) oscillators from a perspective combining modeling, simulation, and experimental observation. Following up on earlier work characterizing the pairwise interaction of Wien-bridge oscillators by Kuramoto-Sakaguchi phase dynamics, we develop a lattice model for a chain thereof, featuring an exponentially decaying spatial kernel. We find that for certain values of the Sakaguchi parameter \(\alpha\), states of traveling phase-domain fronts involving the coexistence of two clearly separated regions of distinct dynamical behavior, can establish themselves in the ring lattice. Experiments and simulations show that stationary coexistence domains of synchronization only manifest themselves with the introduction of a local impurity; here an incoherent cluster of oscillators can arise reminiscent of the chimera states in a range of systems with homogeneous oscillators and suitable nonlocal interactions between them.{
©2017 American Institute of Physics}

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Kuramoto, Y.; Battogtokh, D., Nonlinear Phenom. Complex Syst., 5, 380-385 (2002)
[2] Abrams, D. M.; Strogatz, S. H., Phys. Rev. Lett., 93, 174102 (2004) · doi:10.1103/PhysRevLett.93.174102
[3] Abrams, D. M.; Strogatz, S. H., Int. J. Bifur. Chaos, 16, 21-37 (2006) · Zbl 1101.37319 · doi:10.1142/S0218127406014551
[4] Xie, J.; Knobloch, E.; Kao, H.-C., Phys. Rev. E, 90, 022919 (2014) · doi:10.1103/PhysRevE.90.022919
[5] Laing, C. R., Phys. D, 238, 1569 (2009) · Zbl 1185.34042 · doi:10.1016/j.physd.2009.04.012
[6] Xie, J.; Kao, H.-C.; Knobloch, E., Phys. Rev. E, 91, 032918 (2015) · doi:10.1103/PhysRevE.91.032918
[7] Laing, C. R., Phys. D, 240, 1960 (2011) · Zbl 1262.34038 · doi:10.1016/j.physd.2011.09.009
[8] Laing, C. R., Chaos, 26, 094802 (2016) · Zbl 1382.34043 · doi:10.1063/1.4953663
[9] Kemeth, F. P.; Haugland, S. W.; Schmidt, L.; Kevrekidis, I. G.; Krischer, K., Chaos, 26, 094815 (2016) · doi:10.1063/1.4959804
[10] Panaggio, M. J.; Abrams, D. M., Nonlinearity, 28, R67-R87 (2015) · Zbl 1392.34036 · doi:10.1088/0951-7715/28/3/R67
[11] Martens, E. A.; Thutupalli, S.; Fourriére, A.; Hallatsheck, O., Proc. Natl. Acad. Sci., 110, 10563-10567 (2013) · doi:10.1073/pnas.1302880110
[12] Tinsley, M. R.; Nkomo, S.; Showalter, K., Nat. Phys., 8, 662 (2012) · doi:10.1038/nphys2371
[13] Schmidt, L.; Schönleber, K.; Krischer, K.; García-Morales, V., Chaos, 24, 013102 (2014) · doi:10.1063/1.4858996
[14] Hart, J. D.; Bansal, K.; Murphy, T. E.; Roy, R., Chaos, 26, 094801 (2016) · doi:10.1063/1.4953662
[15] Hagerstrom, A. M.; Murphy, T. E.; Roy, R.; Hövel, P.; Omelchenko, I.; Schöll, E., Nat. Phys., 8, 658-661 (2012) · doi:10.1038/nphys2372
[16] Larger, L.; Penkovsky, B.; Maistrenko, Y., Phys. Rev. Lett., 111, 054103 (2013) · doi:10.1103/PhysRevLett.111.054103
[17] Haugland, S. W.; Schmidt, L.; Krischer, K., Sci. Rep., 5, 09883 (2015) · doi:10.1038/srep09883
[18] Gambuzza, L. V.; Buscarino, A.; Chessari, S.; Fortuna, L.; Meucci, R.; Frasca, M., Phys. Rev. E, 90, 032905 (2014) · doi:10.1103/PhysRevE.90.032905
[19] Rosin, D. P.; Rontani, D.; Haynes, N. D.; Schöll, E.; Gauthier, D. J., Phys. Rev. E, 90, 030902(R) (2014) · doi:10.1103/PhysRevE.90.030902
[20] Temirbayev, A. A.; Zhanabaev, Z. Z.; Tarasov, S. B.; Ponomarenko, V. I.; Rosenblum, M., Phys. Rev. E, 85, 015204 (2012) · doi:10.1103/PhysRevE.85.015204
[21] English, L. Q.; Zeng, Z.; Mertens, D., Phys. Rev. E, 92, 052912 (2015) · doi:10.1103/PhysRevE.92.052912
[22] Sakaguchi, H.; Kuramoto, Y., Prog. Theor. Phys., 76, 576 (1986) · doi:10.1143/PTP.76.576
[23] English, L. Q., Phys. Rev. E, 94, 062212 (2016) · doi:10.1103/PhysRevE.94.062212
[24] da Fonseca, C. M.; Petronilho, J., Linear Algebra Appl., 325, 7 (2001) · Zbl 0983.15007 · doi:10.1016/S0024-3795(00)00289-5
[25] Sandstede, B.; Scheel, A., SIAM J. Appl. Dyn. Sys., 3, 1 (2004) · Zbl 1059.37062 · doi:10.1137/030600192
[26] Xie, J.; Knobloch, E.; Kao, H.-C., Phys. Rev. E, 92, 042921 (2015) · doi:10.1103/PhysRevE.92.042921
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.