The effect of a non-uniform turning kernel on ant trail morphology

Journal of Mathematical Biology

Volumn 49, Issue 4, 2004, Pages 391-432

  Vincent, Andrew D ^a   Myerscough, Mary R ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Ant behaviour; Linear stability analysis; Mathematical modelling; Self organisation

Indexed keywords

PHEROMONE;

ANIMAL; ANIMAL BEHAVIOR; ANT; ARTICLE; BIOLOGICAL MODEL; LOCOMOTION; MATHEMATICS; PHYSIOLOGY;

ANIMALS; ANTS; BEHAVIOR, ANIMAL; LOCOMOTION; MATHEMATICS; MODELS, BIOLOGICAL; PHEROMONES;

FORMICIDAE;

EID: 12944327768     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-003-0201-2     Document Type: Article

References (28)

1. Aron, S., Pasteels, J.M., Deneubourg, J.L.: Trail-laying behaviour during exploratory recruitment in the Argentine ant, Iridomyrmex humilis (Mayr). Biol. Behav. 14, 207-217 (1989)
2. Beckers, R., Deneubourg, J.L., Goss, S.: Trails and U-turns in the selection of a path by the ant Lasius niger. J. Theor. Biol. 159, 397-415 (1992)
3. Beckers, R., Deneubourg, J.L., Goss, S., Pasteels, J.M.: Collective decision making through food recruitment. Insectes Sociaux, Paris 37 (3), 258-267 (1990)
4. Bossert, W.H., Wilson, E.O.: The analysis of olfactory communication among animals. J. Theor. Biol. 5, 443-469 (1963)
5. Bradshaw, J.W.S., Howse, P.E.: Sociochemicals of Ants. In: Bell, W.J. and Cardé, R.T. (eds) Chemical Ecology of Insects. Chapman and Hall, London (1984)
6. Camazine, S., Sneyd, J.: A model of collective nectar source selection by honey bees. J. Theor. Biol. 149, 547-571 (1991)
7. Cox, M., Myerscough, M.R.: A flexible model of foraging by a honey bee colony: The effects of individual behaviour on foraging success. J. Theor. Biol., 223, 179-197
8. Deneubourg, J.L., Aron, S., Goss, S., Pasteels, J.M.: The self-organising exploratory pattern of the Argentine Ant. J. Insect Behav. 3(2), 159-168 (1990)
9. Deneubourg, J.L., Goss, S., Franks, N., Pasteels, J.M.: The blind leading the blind: chemically mediated mophogenesis and Army Ant raid patterns. J. Insect Behav. 2, 719-725 (1989)
10. Edelstein-Keshet, L.: Simple models for trail-following behaviour: trunk trails versus individual foragers. J. Math. Biol. 32, 303-328 (1994)
11. Edelstein-Keshet, L., Ermentrout, G.B.: Models for contact-mediated pattern formation: cells that form parallel arrays. J. Math. Biol. 29, 33-58 (1990)
12. Franks, N.R., Gomez, N., Goss, S., Deneubourg, J.L.: The blind leading the blind in Army Ant raid patterns: testing a model of self-organization (Hymenoptera: Formicidae). J. Insect Behav. 4, 583-607 (1991)
13. Heinrich, B.: The mechanisms and energetics of honeybee swarm temperature regulation. J. exp. Biol. 91, 25-55 (1981)
14. Millonas, M.M.: A connectionist type model of self-organized foraging and emergent behavior in ant swarms. J. Theor. Biol. 159, 529-552 (1992)
15. Millonas, M.: Swarms, Phase Transitions and Collective Intelligence. In: Langton, C.G. (ed.) Artificial Life III: Studies in the Sciences of Complexity, Proc Vol. XVII, Addison-Wesley (1994)
16. Mogilner, A., Edelstein-Keshet, E.: Selecting a common direction. J. Math. Biol. 33, 619-660 (1995)
17. Myerscough, M.R.: A simple model for thermoregulation in honeybee swarms. J. Theor. Biol. 162, 381-393 (1993)
18. Nicolis, S.C., Deneubourg, J.L.: Emerging patterns and food recruitment in ants: an analytical study. J. Theor. Biol. 198, 575-592 (1999)
19. O'Toole, D.V., Robinson, P.A., Myerscough, M.R.: Self-organized criticality in termite architecture: a role for crowding in ensuring ordered nest expansion. J. Thoer. Biol. 198, 305-327 (1999)
20. Pasteels, J.M.P., Deneubourg, J.L., Verhaeghe, J.C., Boeve, J.L., Quinet, Y.: Orientation along terrestrial trails by ants. In: Payne, T., Birch, M. (eds) Mechanisms in Insect Olfaction, 131-138. Oxford Univ. Press (1986)
21. Rauch, E.M., Millonas, M.M., Chialvo, D.R.: Pattern formation and functionality in swarm models. Phys. Lett. A 207, 185-193 (1995)
22. Schneirla, T.C., Reyes, A.Y.: Rading and related behaviour in two surface adapted species of the old world doryline ant Aenictus. Animal Behaviour 14, 132-148 (1966)
23. Schweitzer, F., Lau, K., Family, F.: Active random walkers simulate trunk trail formation by ants. Biosys 41, 153-166 (1997)
24. Seneta, E.: Non-negative Matrices and Markov Chains. Springer-Verlag, New York (1980)
25. Theraulaz, G., Bonabeau, E.: Modelling the collective building of complex architectures in social insects with lattice swarms. J. Theor. Biol. 177, 381-400 (1995)
26. Watmough, J., Camazine, S.: Self-organized thermoregulation of honeybee clusters. J. Theor. Biol. 176, 391-402 (1995)
27. Watmough, J., Edelstein-Keshet, L.: A one-dimensional model of trail propagation by army ants. J. Math. Biol. 33, 459-476 (1995a)
28. Watmough, J., Edelstein-Keshet, L.: Modelling the formation of trail networks by foraging ants. J. Theor. Biol. 176, 357-371 (1995b)