Oscillators that sync and swarm

Abstract

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact.

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References 70

1. 1.

   Winfree AT. Biological rhythms and the behavior of populations of coupled oscillators. J. Theor. Biol. 1967;16:15-42.

   Not in our library10.1016/0022-5193(67)90051-3

2. 2.

   Kuramoto, Y. in International Symposium on Mathematical Problems in Theoretical Physics (ed. Araki, H.) 420–422 (Springer, Berlin, 1975).

   Not in our library

3. 3.

   Strogatz, S. Sync: The emerging science of spontaneous order (Hyperion, New York, 2003).

   Not in our library

4. 4.

   Pikovsky, A., Rosenblum, M. & Kurths, J. Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, UK, 2003).

   Not in our library

5. 5.

   Acebrón JA, Bonilla LL, Vicente CJP, Ritort F, Spigler R. The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 2005;77:137.

   Not in our library10.1103/revmodphys.77.137

6. 6.

   Aihara I, Kitahata H, Yoshikawa K, Aihara K. Mathematical modeling of frogs calling behavior and its possible application to artificial life and robotics. Artif. Life Robot. 2008;12:29-32.

   Not in our library10.1007/s10015-007-0436-x

7. 7.

   Montbrió E, Pazó D, Roxin A. Macroscopic description for networks of spiking neurons. Phys. Rev. X. 2015;5:021028.

   Not in our library

8. 8.

   Pazó D, Montbrió E. Low-dimensional dynamics of populations of pulse-coupled oscillators. Phys. Rev. X. 2014;4:011009.

   Not in our library

9. 9.

   O’Keeffe KP, Strogatz SH. Dynamics of a population of oscillatory and excitable elements. Phys. Rev. E. 2016;93:062203.

   Not in our library10.1103/physreve.93.062203

10. 10.

    Luke TB, Barreto E, So P. Macroscopic complexity from an autonomous network of networks of theta neurons. Front. Comput. Neurosci. 2014;8:145.

    Not in our library10.3389/fncom.2014.00145

11. 11.

    Laing CR. Derivation of a neural field model from a network of theta neurons. Phys. Rev. E. 2014;90:010901.

    Not in our library10.1103/physreve.90.010901

12. 12.

    Néda Z, Ravasz E, Vicsek T, Brechet Y, Barabási AL. Physics of the rhythmic applause. Phys. Rev. E. 2000;61:6987-6992.

    Not in our library10.1103/physreve.61.6987

13. 13.

    Daido H. Lower critical dimension for populations of oscillators with randomly distributed frequencies: a renormalization-group analysis. Phys. Rev. Lett. 1988;61:231.

    Not in our library10.1103/physrevlett.61.231

14. 14.

    Östborn P. Renormalization of oscillator lattices with disorder. Phys. Rev. E. 2009;79:051114.

    Not in our library10.1103/physreve.79.051114

15. 15.

    Hong H, Chaté H, Park H, Tang L-H. Entrainment transition in populations of random frequency oscillators. Phys. Rev. Lett. 2007;99:184101.

    Not in our library10.1103/physrevlett.99.184101

16. 16.

    Hong H, Chaté H, Tang L-H, Park H. Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model. Phys. Rev. E. 2015;92:022122.

    Not in our library10.1103/physreve.92.022122

17. 17.

    Pantaleone J. Stability of incoherence in an isotropic gas of oscillating neutrinos. Phys. Rev. D. 1998;58:073002.

    Not in our library10.1103/physrevd.58.073002

18. 18.

    Wiesenfeld K, Colet P, Strogatz SH. Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett. 1996;76:404.

    Not in our library10.1103/physrevlett.76.404

19. 19.

    Motter AE, Myers SA, Anghel M, Nishikawa T. Spontaneous synchrony in power-grid networks. Nat. Phys. 2013;9:191-197.

    Not in our library10.1038/nphys2535

20. 20.

    Dorfler F, Bullo F. Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators. SIAM J. Control Optim. 2012;50:1616-1642.

    Not in our library10.1137/110851584

21. 21.

    Strogatz SH, Abrams DM, McRobie A, Eckhardt B, Ott E. Theoretical mechanics: Crowd synchrony on the Millennium Bridge. Nature. 2005;438:43-44.

    Not in our library10.1038/438043a

22. 22.

    Couzin I. Collective minds. Nature. 2007;445:715-715.

    Not in our library10.1038/445715a

23. 23.

    Buhl J, et al. From disorder to order in marching locusts. Science. 2006;312:1402-1406.

    Not in our library10.1126/science.1125142

24. 24.

    Sumpter, D. J. Collective Animal Behavior (Princeton University Press, Princeton, NJ, 2010).

    Not in our library

25. 25.
    Understanding how animal groups achieve coordinated movement · 2016

    No notice
26. 26.

    Ballerini M, et al. Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl Acad. Sci. USA. 2008;105:1232-1237.

    Not in our library10.1073/pnas.0711437105

27. 27.

    Bialek W, et al. Statistical mechanics for natural flocks of birds. Proc. Natl Acad. Sci. USA. 2012;109:4786-4791.

    Not in our library10.1073/pnas.1118633109

28. 28.

    Reynolds CW. Flocks, herds and schools: a distributed behavioral model. ACM SIGGRAPH Comp. Graph. 1987;21:25-34.

    Not in our library10.1145/37402.37406

29. 29.

    Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 1995;75:1226.

    Not in our library10.1103/physrevlett.75.1226

30. 30.

    Bernoff AJ, Topaz CM. Nonlocal aggregation models: a primer of swarm equilibria. SIAM Rev. 2013;55:709-747.

    Not in our library10.1137/130925669

31. 31.

    Topaz CM, Bertozzi AL. Swarming patterns in a two-dimensional kinematic model for biological groups. SIAM J. Appl. Math. 2004;65:152-174.

    Not in our library10.1137/s0036139903437424

32. 32.

    Topaz CM, Bertozzi AL, Lewis MA. A nonlocal continuum model for biological aggregation. Bull. Math. Biol. 2006;68:1601-1623.

    Not in our library10.1007/s11538-006-9088-6

33. 33.

    Kolokolnikov T, Sun H, Uminsky D, Bertozzi AL. Stability of ring patterns arising from two-dimensional particle interactions. Phys. Rev. E. 2011;84:015203.

    Not in our library10.1103/physreve.84.015203

34. 34.

    Uriu K, Ares S, Oates AC, Morelli LG. Dynamics of mobile coupled phase oscillators. Phys. Rev. E. 2013;87:032911.

    Not in our library10.1103/physreve.87.032911

35. 35.

    Belykh IV, Belykh VN, Hasler M. Blinking model and synchronization in small-world networks with a time-varying coupling. Phys. D. 2004;195:188-206.

    Not in our library10.1016/j.physd.2004.03.013

36. 36.

    Stilwell DJ, Bollt EM, Roberson DG. Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J. Appl. Dynam. Syst. 2006;5:140-156.

    Not in our library10.1137/050625229

37. 37.

    Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S. Synchronization of moving chaotic agents. Phys. Rev. Lett. 2008;100:044102.

    Not in our library10.1103/physrevlett.100.044102

38. 38.

    Fujiwara N, Kurths J, Daz-Guilera A. Synchronization in networks of mobile oscillators. Phys. Rev. E. 2011;83:025101.

    Not in our library10.1103/physreve.83.025101

39. 39.

    Walker TJ. Acoustic synchrony: two mechanisms in the snowy tree cricket. Science. 1969;166:891-894.

    Not in our library10.1126/science.166.3907.891

40. 40.

    Greenfield MD. Synchronous and alternating choruses in insects and anurans: common mechanisms and diverse functions. Am. Zool. 1994;34:605-615.

    Not in our library10.1093/icb/34.6.605

41. 41.

    Aihara I, et al. Spatio-temporal dynamics in collective frog choruses examined by mathematical modeling and field observations. Sci. Rep. 2014;4:3891.

    Not in our library10.1038/srep03891

42. 42.

    Yan J, Bloom M, Bae SC, Luijten E, Granick S. Linking synchronization to self-assembly using magnetic Janus colloids. Nature. 2012;491:578-581.

    Not in our library10.1038/nature11619

43. 43.

    Snezhko A, Aranson IS. Magnetic manipulation of self-assembled colloidal asters. Nat. Mater. 2011;10:698-703.

    Not in our library10.1038/nmat3083

44. 44.

    Martin JE, Snezhko A. Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields. Rep. Prog. Phys. 2013;76:126601.

    Not in our library10.1088/0034-4885/76/12/126601

45. 45.

    Nguyen NH, Klotsa D, Engel M, Glotzer SC. Emergent collective phenomena in a mixture of hard shapes through active rotation. Phys. Rev. Lett. 2014;112:075701.

    Not in our library10.1103/physrevlett.112.075701

46. 46.

    van Zuiden, B. C., Paulose, J., Irvine, W. T., Bartolo, D. & Vitelli, V. Spatiotemporal order and emergent edge currents in active spinner materials. Proc. Natl Acad. Sci. USA113, 12919–12924 (2016).

    Not in our library10.1073/pnas.1609572113

47. 47.

    Igoshin OA, Mogilner A, Welch RD, Kaiser D, Oster G. Pattern formation and traveling waves in myxobacteria: theory and modeling. Proc. Natl Acad. Sci. USA. 2001;98:14913-14918.

    Not in our library10.1073/pnas.221579598

48. 48.

    Tanaka D. General chemotactic model of oscillators. Phys. Rev. Lett. 2007;99:134103.

    Not in our library10.1103/physrevlett.99.134103

49. 49.

    Iwasa M, Iida K, Tanaka D. Hierarchical cluster structures in a one-dimensional swarm oscillator model. Phys. Rev. E. 2010;81:046220.

    Not in our library10.1103/physreve.81.046220

50. 50.

    Fetecau RC, Huang Y, Kolokolnikov T. Swarm dynamics and equilibria for a nonlocal aggregation model. Nonlinearity. 2011;24:2681.

    Not in our library10.1088/0951-7715/24/10/002

51. 51.

    Carrillo J, D’orsogna M, Panferov V. Double milling in self-propelled swarms from kinetic theory. Kinet. Relat. Mod. 2009;2:363-378.

    Not in our library10.3934/krm.2009.2.363

52. 52.

    Riedel IH, Kruse K, Howard J. A self-organized vortex array of hydrodynamically entrained sperm cells. Science. 2005;309:300-303.

    Not in our library10.1126/science.1110329

53. 53.

    Hong H, Strogatz SH. Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys. Rev. Lett. 2011;106:054102.

    Not in our library10.1103/physrevlett.106.054102

54. 54.

    Hong H, O’Keeffe KP, Strogatz SH. Phase coherence induced by correlated disorder. Phys. Rev. E. 2016;93:022219.

    Not in our library10.1103/physreve.93.022219

55. 55.

    Pohl O, Stark H. Dynamic clustering and chemotactic collapse of self-phoretic active particles. Phys. Rev. Lett. 2014;112:238303.

    Not in our library10.1103/physrevlett.112.238303

56. 56.

    Maude A. Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature. 1963;200:381.

    Not in our library10.1038/200381a0

57. 57.

    Elgeti J, Gompper G. Emergence of metachronal waves in cilia arrays. Proc. Natl Acad. Sci. USA. 2013;110:4470-4475.

    Not in our library10.1073/pnas.1218869110

58. 58.

    Okada Y, et al. Abnormal nodal flow precedes situs inversus in iv and inv mice. Mol. Cell. 1999;4:459-468.

    Not in our library10.1016/s1097-2765(00)80197-5

59. 59.

    Wong L, Miller IF, Yeates DB. Nature of the mammalian ciliary metachronal wave. J. Appl. Physiol. 1993;75:458-467.

    Not in our library10.1152/jappl.1993.75.1.458

60. 60.

    Lauga E, Powers TR. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 2009;72:096601.

    Not in our library10.1088/0034-4885/72/9/096601

61. 61.

    Immler S, Moore HD, Breed WG, Birkhead TR. By hook or by crook? Morphometry, competition and cooperation in rodent sperm. PLoS ONE. 2007;2:e170.

    Not in our library10.1371/journal.pone.0000170

62. 62.

    Moore H, Dvoráková K, Jenkins N, Breed W. Exceptional sperm cooperation in the wood mouse. Nature. 2002;418:174-177.

    Not in our library10.1038/nature00832

63. 63.

    Taylor, G. Analysis of the swimming of microscopic organisms. in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 209, 447–461 (The Royal Society, London, UK, 1951).

    Not in our library

64. 64.

    Fauci LJ, McDonald A. Sperm motility in the presence of boundaries. Bull. Math. Biol. 1995;57:679-699.

    Not in our library10.1007/bf02461846

65. 65.

    Yang Y, Elgeti J, Gompper G. Cooperation of sperm in two dimensions: synchronization, attraction, and aggregation through hydrodynamic interactions. Phys. Rev. E. 2008;78:061903.

    Not in our library10.1103/physreve.78.061903

66. 66.

    Hayashi F. Insemination through an externally attached spermatophore: bundled sperm and post-copulatory mate guarding by male fishflies (megaloptera: Corydalidae). J. Insect. Physiol. 1996;42:859-866.

    Not in our library10.1016/0022-1910(96)00037-6

67. 67.

    Leoni M, Liverpool T. Synchronization and liquid crystalline order in soft active fluids. Phys. Rev. Lett. 2014;112:148104.

    Not in our library10.1103/physrevlett.112.148104

68. 68.

    Starnini, M., Frasca, M. & Baronchelli, A. Emergence of metapopulations and echo chambers in mobile agents. Sci. Rep. 6, 31834 (2016).

    Not in our library10.1038/srep31834

69. 69.

    Kruk, N., Maistrenko, Y., Wenzel, N. & Koeppl, H. Self-propelled chimeras. arXiv preprint arXiv:1511.04738 (2015).

    Not in our library

70. 70.

    Liebchen B, Levis D. Collective behavior of chiral active matter: pattern formation and enhanced flocking. Phys. Rev. Lett. 2017;119:05800.

    Not in our library10.1103/physrevlett.119.058002

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