Geodesic
Solitary states in a 2D lattice of bistable elements with global and close to global interaction
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 317-329.

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This paper is concerned with the spatiotemporal dynamics of the 2D lattice of cubic maps with nonlocal coupling. Different types of chimera structures have been found. Also, the underexplored regime of solitary states has been found. It is shown that the solitary states are typical of a large coupling radius. The possibility of detecting such a regime increases with the transition to global interaction, while chimera states disappear.
Mots-clés : oscillator ensemble, nonlocal interaction, spatial structure
Keywords: 2D lattice, global coupling, chimera state, solitary state. 
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I. A. Shepelev; T. E. Vadivasova. Solitary states in a 2D lattice of bistable elements with global and close to global interaction. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 317-329. http://geodesic.mathdoc.fr/item/ND_2017_13_3_a1/

[1] Abrams D. M., Mirollo R., Strogatz S. H., Wiley D. A., “Solvable model for chimera states of coupled oscillators”, Phys. Rev. Lett., 101:8 (2008), 084103, 4 pp. | DOI

[2] Abrams D. M., Strogatz S. H., “Chimera states for coupled oscillators”, Phys. Rev. Lett., 93:17 (2004), 174102, 4 pp. | DOI

[3] Afraimovich V. S., Nekorkin V. I., Osipov G. V., Shalfeev V. D., Stability, structures and chaos in nonlinear synchronization networks, World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises, 6, World Sci., River Edge, N.J., 1994, 246 pp. | MR | Zbl

[4] Bogomolov S. A., Slepnev A. V., Strelkova G. I., Schöll E., Anishchenko V. S., “Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems”, Commun. Nonlinear Sci. Numer. Simul., 43 (2016), 25–36 | DOI | MR

[5] Belykh V. N., Belykh I. V., Mosekilde E., “Cluster synchronization modes in an ensemble of coupled chaotic oscillators”, Phys. Rev. E, 63:3 (2001), 036216, 4 pp. | DOI | MR

[6] Bogomolov S. A., Strelkova G. I., Schöll E., Anishchenko V. S., “Amplitude and phase chimeras in an ensemble of chaotic oscillators”, Tech. Phys. Lett., 42:7 (2016), 765–768 | DOI

[7] Böhm F., Zakharova A., Schöll E., Lüdge K., “Amplitude-phase coupling drives chimera states in globally coupled laser networks”, Phys. Rev. E, 91:4 (2015), 040901, 6 pp. | DOI | MR

[8] Clerc M. G., Coulibaly S., Ferré M. A., García-Ñustes M. A., Rojas R. G., “Chimera-type states induced by local coupling”, Phys. Rev. E, 93:5 (2015), 052204, 5 pp. | DOI

[9] Epstein I. R., Pojman J. A., An introduction to nonlinear chemical dynamics: Oscillations, waves, patterns, and chaos, Oxford Univ. Press, New York, 1998, 408 pp. | MR

[10] Hagerstrom A. M., Murphy Th. E., Roy R., Hövel Ph., Omelchenko I., Schöll E., “Experimental observation of chimeras in coupled-map lattices”, Nature Phys., 8:9 (2012), 658–661 | DOI

[11] Hizanidis J., Lazarides N., Neofotistos G., Tsironis G. P., “Chimera states and synchronization in magnetically driven SQVID metamaterials”, Eur. Phys. J. Special Topics, 225:6–7 (2016), 1231–1243 | DOI

[12] Jaros P., Maistrenko Yu., Kapitaniak T., “Chimera states on the route from coherence to rotating waves”, Phys. Rev. E, 91:2 (2015), 022907, 5 pp. | DOI

[13] Kaneko K., “Pattern dynamics in spatiotemporal chaos: Pattern selection, diffusion of defect and pattern competition intermittency”, Phys. D, 34:1–2 (1989), 1–41 | DOI | MR | Zbl

[14] Kaneko K., “Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements”, Phys. D, 41:2 (1990), 137–172 | DOI | MR | Zbl

[15] Kapitaniak T., Kuzma P., Wojewoda J., Czolczynski K., Maistrenko Yu., “Imperfect chimera states for coupled pendula”, Sci. Rep., 4 (2014), 6379, 4 pp. | DOI

[16] Kuramoto Y., Chemical oscillations, waves, and turbulence, Springer Series in Synergetics, 19, Springer, Berlin, 1984, 158 pp. | MR | Zbl

[17] Kuramoto Y., Battogtokh D., “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators”, Nonl. Phen. Compl. Sys., 5:4 (2002), 380–385

[18] Kuznetsov A. P., Kuznetsov S. P., “Critical dynamics of coupled map lattices at the onset of chaos”, Radiophys. Quantum El., 34:10–12 (1991), 845–868 | MR

[19] Laing C. R., “Chimera in networks with purely local coupling”, Phys. Rev. E, 92:5 (2015), 050904, 5 pp. | DOI

[20] Landa P. S., Nonlinear oscillations and waves in dynamical systems, Math. Appl., 360, Springer, Dordrecht, 2013, XV, 544 pp. | MR | MR

[21] Maistrenko Yu., Penkovsky B., Rosenblum M., “Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction”, Phys. Rev. E, 89:6 (2014), 060901, 5 pp. | DOI | MR

[22] Maistrenko Yu., Sudakov O., Osiv O., Maistrenko V., “Chimera states in three dimensions”, New J. Phys., 17:7 (2015), 073037 | DOI

[23] Malchow H., Petrovskii S. V., Venturino E., Spatiotemporal patterns in ecology and epidemiology: Theory, models, and simulation, Chapman and Hall/CRC, London, 2007, 464 pp. | MR

[24] Martens E. A., Thutupalli S., Fourrière A., Hallatschek O., “Chimera states in mechanical oscillator networks”, Proc. Natl. Acad. Sci., 110:26 (2013), 10563–10567 | DOI

[25] Mikhailov A. S., Loskutov A. Yu., Foundation of synergetics 2: Complex patterns, Springer Series in Synergetics, 52, Springer, Berlin, 1995, 210 pp. | MR

[26] Nekorkin V. I., Velarde M. G., Synergetic phenomena in active lattices: Patterns, waves, solitons, chaos, Springer Series in Synergetics, Springer, Berlin, 2002, 357 pp. | DOI | MR | Zbl

[27] Omelchenko I., Maistrenko Yu., Hövel Ph., Schöll E., “Loss of coherence in dynamical networks: Spatial chaos and chimera states”, Phys. Rev. Lett., 106:23 (2011), 234102, 4 pp. | DOI

[28] Omelchenko I., Provata A., Hizanidis J., Schöll E., Hövel Ph., “Robustness of chimera states for coupled FitzHugh – Nagumo oscillators”, Phys. Rev. E, 91:2 (2015), 022917, 13 pp. | DOI | MR

[29] Omelchenko I., Riemenschneider B., Hövel Ph., Schöll E., “Transition from spatial coherence to incoherence in coupled chaotic systems”, Phys. Rev. E, 85:2 (2012), 026212, 9 pp. | DOI | MR

[30] Omelchenko I., Omel'chenko O. E., Hövel Ph., Schöll E., “When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states”, Phys. Rev. Lett., 110:22 (2013), 224101, 5 pp. | DOI

[31] Omel’chenko O. E., Wolfrum M., Yanchuk S., Maistrenko Yu. L., Sudakov O., “Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators”, Phys. Rev. E, 85:3 (2012), 036210, 5 pp. | DOI | MR

[32] Osipov G. V., Kurths J., Zhou Ch., Synchronization in oscillatory networks, Springer, Berlin, 2007, 370 pp. | MR | Zbl

[33] Panaggio M. J., Abrams D. M., “Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators”, Nonlinearity, 28:3 (2015), R67–R87 | DOI | MR | Zbl

[34] Pikovsky A., Rosenblum M., Kurths J., Synchronization: A universal concept in nonlinear sciences, Cambridge Nonlinear Sci. Ser., 12, Cambridge Univ. Press, New York, 2001, 432 pp. | MR | Zbl

[35] Schmidt L. T., Schönleber K., Krischer K., García-Morales V., “Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling”, Chaos, 24:1 (2014), 013102, 7 pp. | DOI | MR

[36] Semenova N., Zakharova A., Schöll E., Anishchenko V., “Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators?”, Europhys. Lett., 112:4 (2015), 40002, 6 pp. | DOI | MR

[37] Sethia G. C., Sen A., “Chimera states: The existence criteria revisited”, Phys. Rev. Lett., 112:14 (2014), 144101, 5 pp. | DOI

[38] Shepelev I. A., Zakharova A., Vadivasova T. E., “Chimera regimes in a ring of oscillators with local nonlinear interaction”, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 277–283 | DOI | MR

[39] Smart A. G., “Exotic chimera dynamics glimpsed in experiments”, Phys. Today, 65:10 (2012), 17–19 | DOI

[40] Tinsley M. R., Nkomo S., Showalter K., “Chimera and phase-cluster states in populations of coupled chemical oscillators”, Nature Phys., 8 (2012), 662–665 | DOI

[41] Vadivasova T. E., Strelkova G. I., Bogomolov S. A., Anishchenko V. S., “Correlation analysis of the coherence-incoherence transition in a ring of nonlocally coupled logistic maps”, Chaos, 26:9 (2016), 093108, 9 pp. | DOI | MR

[42] Vüllings A., Hizanidis J., Omelchenko I., Hövel Ph., “Clustered chimera states in systems of type-I excitability”, New J. Phys., 16:12 (2014), 123039 | DOI

[43] Wolfrum M., Omel’chenko O. E., Yanchuk S., Maistrenko Yu. L., “Spectral properties of chimera states”, Chaos, 21:1 (2011), 013112, 8 pp. | DOI | MR | Zbl

[44] Yeldesbay A., Pikovsky A., Rosenblum M., “Chimeralike states in an ensemble of globally coupled oscillators”, Phys. Rev. Lett., 112:14 (2014), 144103, 5 pp. | DOI

[45] Zakharova A., Kapeller M., Schöll E., “Chimera death: Symmetry breaking in dynamical networks”, Phys. Rev. Lett., 112:15 (2014), 154101, 5 pp. | DOI