A conceptual model for milling formations in biological aggregates

Bulletin of Mathematical Biology

Volumn 71, Issue 2, 2009, Pages 352-382

  Lukeman, Ryan ^a   Li, Yue Xian ^a   Edelstein Keshet, Leah ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Collective motion; Milling; Schooling behavior; Self organization; Self propelled particles

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COOPERATION; CROWDING; FLYING; GROUP PROCESS; POPULATION DYNAMICS; POPULATION MIGRATION; ROTATION; SYSTEM ANALYSIS; SYSTEMS THEORY;

ANIMAL MIGRATION; ANIMALS; COOPERATIVE BEHAVIOR; FLIGHT, ANIMAL; GROUP PROCESSES; MASS BEHAVIOR; MODELS, BIOLOGICAL; POPULATION DYNAMICS; ROTATION; SYSTEMS INTEGRATION; SYSTEMS THEORY;

EID: 58349121197     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9365-7     Document Type: Article

References (35)

1. E. Ben-Jacob 1997 Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development Physica A 238 181 197
2. Camazine, S., et al., 2001. Self-Organization in Biological Systems, Princeton University Press, Princeton.
3. Y.L. Chuang 2007 State transitions and the continuum limit for a 2d interacting, self-propelled particle system Physica D 232 33 47
4. I.D. Couzin 2002 Collective memory and spatial sorting in animal groups J. Theor. Biol. 218 1 11
5. Z. Csahók A. Czirók 2008 Hydrodynamics of bacterial motion Physica A 243 304 318
6. A. Czirók 1996 Formation of complex bacterial colonies via self-generated vortices Phys. Rev. E 54 2 1792 1801
7. Davis, P.J., 1979. Circulant Matrices, Wiley, New York.
8. M.R. D'Orsogna 2006 Self-propelled particles with soft-core interactions: Patterns, stability, and collapse Phys. Rev. Lett. 96 104302
9. D. Grossman I.S. Aranson E. Ben-Jacob 2008 Emergence of agent swarm migration and vortex formation through inelastic collisions New J. Phys. 10 023036
10. C.J. Harvey-Clark 1999 Putative mating behavior in basking sharks off the Nova Scotia coast Copeia 3 780 782
11. J. Hemmingsson 1995 Modellization of self-propelling particles with a coupled map lattice model J. Phys. A 28 4245 4250
12. A. Huth C. Wissel 1992 The simulation of movement of fish schools J. Theor. Biol. 156 365 385
13. V.L. Kulinskii 2005 Hydrodynamic model for a system of self-propelling particles with conservative kinematic constraints Europhys. Lett. 71 2 207 213
14. H. Levine W. Rappel I. Cohen 2001 Self-organization in systems of self-propelled particles Phys. Rev. E 63 017101
15. Y.-X. Li R. Lukeman L. Edelstein-Keshet 2008 Minimal mechanisms for school formation in self-propelled particles Physica D 237 5 699 720
16. R. Mach F. Schweitzer 2007 Modeling vortex swarming in daphnia Bull. Math. Biol. 69 2 539 562
17. J.A. Marshall M.E. Broucke B.A. Francis 2004 Formations of vehicles in cyclic pursuit IEEE Trans. Automat. Contr. 49 11 1963 1974
18. A. Mogilner 2003 Mutual interactions, potentials, and individual distance in a social aggregation J. Math. Biol. 47 353 389
19. H.-S. Niwa 1994 Self-organizing dynamic model of fish schooling J. Theor. Biol. 171 123 136
20. H.-S. Niwa 1996 Newtonian dynamical approach to fish schooling J. Theor. Biol. 181 47 63
21. H.-S. Niwa 1998 Migration of fish schools in heterothermal environments J. Theor. Biol. 193 215 231
22. Okubo, A., 1980. Diffusion and Ecological Problems: Mathematical Models, Springer, New York.
23. Okubo, A., Grunbaum, D., Edelstein-Keshet, L., 2001. The dynamics of animal grouping. In: Okubo, A., Levin, S. (Eds.), Diffusion and Ecological Problems: Modern Perspectives. Springer, New York
24. A.E. Parr 1927 A contribution to the theoretical analysis of the schooling behaviour of fishes Occ. Pap. Bingham Oceanogr. Collect. 1 1 32
25. J. Parrish L. Edelstein-Keshet 1999 Complexity, pattern, and evolutionary trade-offs in animal aggregation Science 284 99 101
26. J. Parrish S. Viscido D. Grunbaum 2002 Self-organized fish schools: an examination of emergent properties Biol. Bull. 202 296 305
27. V.I. Ratushnaya 2007 Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints J. Phys. A 40 2573 2581
28. S. Sakai 1973 A model for group structure and its behavior Biophys. Jpn. 13 82 90
29. T.C. Schneirla 1944 A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation Am. Mus. Novit. 1253 1 25
30. J.R. Silvester 2000 Determinants of block matrices Math. Gaz. 84 460 467
31. R. Suzuki S. Sakai 1973 Movement of a group of animals Biophys. Jpn. 13 281 282
32. C. Topaz A. Bertozzi 2004 Swarming patterns in a two-dimensional kinematic model for biological groups SIAM J. Appl. Math. 65 1 152 174
33. T. Vicsek 1995 Novel type of phase transition in a system of self-driven particles Phys. Rev. Lett. 75 6 1226 1229
34. D. Weihs 1974 Energetic advantages of burst swimming of fish J. Theor. Biol. 48 215 229
35. S.G. Wilson 2004 Basking sharks schooling in the southern Gulf of Maine Fish. Oceanogr. 13 283 286