Abstract
The formation of droplets of ants Linepithema humile (Mayr) is observed under certain experimental conditions: a fluctuating aggregate forms at the end of a rod and a droplet containing up to 40 ants eventually falls down. When the flux of incoming ants is sufficient, this process can continue for several hours, leading to the formation and fall of tens of droplets. Previous work indicates that the time series of drop-to-drop intervals may result from a nonlinear low-dimensional dynamics, and the interdrop increments exhibit long-range anticorrelations. A model of aggregation and droplet formation, based on experimental observations, is introduced and shown to reproduce these properties.
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References
Austin, J. (1991). A mechanical treatment of the leaky faucet experiment. Phys. Lett. A 155, 148–154.
Bonabeau, E., G. Theraulaz, J. L. Deneubourg, S. Aron and S. Camazine (1997). Self-organization in social insects. TREE 12, 188–193.
Bonabeau, E., G. Theraulaz, J. L. Deneubourg, N. Franks, O. Rafelsberger, J. L. Joly and S. Blanco (1998a). A model for the emergence of pillars, walls and royal chamber in termite nests. Phil. Trans. R. Soc. B 353, 1561–1576.
Bonabeau, E., G. Theraulaz, J.-L. Deneubourg, A. Lioni, F. Libert, C. Sauwens and L. Passera (1998b). Dripping faucet with ants. Phys. Rev. E 57, 5904–5907.
Buldyrev, S. V., A. L. Goldberger, S. Havlin, C.-K. Peng and H. E. Stanley (1994). Fractals in biology and medicine: from DNA to the heartbeat, in Fractals in Science, A. Bunde and S. Havlin (Eds), Berlin: Springer, pp. 49–87.
Buschinger, A. and U. Maschwitz (1984). Defensive behavior and defensive mechanisms in ants, in Defensive Mechanisms in Social Insects, H. R. Hermann (Ed.), New York: Praeger Scientific, pp. 95–150.
Camazine, S., J. L. Deneubourg, N. Franks, J. Sneyd, G. Theraulaz and E. Bonabeau (2001). Self-Organization in Biological Systems, Princeton: Princeton University Press.
Cole, B. J. (1991a). Is animal behaviour chaotic? Evidence from the activity of ants. Proc. R. Soc. B 244, 253–259.
Cole, B. J. (1991b). Short term activity cycles in ants generation of periodicity by worker interaction. Am. Nat. 137, 244–259.
Darchen, R. (1959). Les techniques de construction chez Apis Mellifica. Ann. des Sc. Nat., Zool. 1, 111–209.
Deneubourg, J.-L. (1977). Application de l’ordre par fluctuations á la description de certaines étapes de la construction du nid chez les termites. Ins. Soc. 24, 117–130.
Deneubourg, J.-L. and S. Goss (1989). Collective patterns and decision making. Ethol. Ecol. Evol. 1, 295–311.
Franks, N. R. (1989). Army ants: a collective intelligence. Am. Sci. 77, 138–145.
Franks, N. R., S. Bryant, R. Griffiths and L. Hemerik (1990). Synchronization of the behaviour within nest of the ant Leptothorax acervorum (Fabricus)-I. Discovering the phenomenon and its relation to the level of starvation. Bull. Math. Biol. 52, 597–612.
Goss, S. and J. L. Deneubourg (1988). Autocatalysis as a source of synchronised rhythmical activity in social insects. Ins. Soc. 35, 310–315.
Havlin, S., R. B. Selinger, M. Schwartz, H. E. Stanley and A. Bunde (1988). Random multiplicative processes and transport in structures with correlated spatial disorder. Phys. Rev. Lett. 61, 1438–1441.
Hölldobler, B. and E. O. Wilson (1977). Weaver ants. Sci. Am. 237, 146–154.
Hölldobler, B. and E. O. Wilson (1978). The multiple recruitment systems of the African weaver ant Oecophylla longinoda (Latreille) (Hymenoptera: Formicidae). Behav. Ecol. Sociobiol 3, 19–60.
Hölldobler, B. and E. O. Wilson (1990). The Ants, Cambridge, MA: Harvard University Press.
Martien, P., S. C. Pope, P. L. Scott and R. S. Shaw (1985). The chaotic behavior of the leaky faucet. Phys. Lett. A 110, 399–404.
Peng, C.-K., J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley and A. L. Goldberger (1993). Long-range anticorrelations and non-gaussian behavior of the heartbeat. Phys. Rev. Lett. 70, 1343–1346.
Penna, T. J. P., P. M. C. de Oliveira, J. C. Sartorelli, W. M. Gonçalves and R. D. Pinto (1995). Long-range anticorrelations and non-gaussian behavior of a leaky faucet. Phys. Rev. E 52, 2168–2171.
Pradhan, N. and P. K. Sadavisan (1997). Validity of dimensional complexity measures of EEG signals. Int. J. Bifurcation Chaos 7, 173–186.
Sanchez-Ortiz, G. I. and A. L. Salas-Brito (1995). Strange attractors in a relaxation oscillator model for the dripping water faucet. Phys. Lett. A 203, 300–311.
Sartorelli, J. C., W. M. Gonçalves and R. D. Pinto (1994). Crisis and intermittence in a leaky-faucet experiment. Phys. Rev. E 49, 3963–3975.
Shaw, R. S. (1984). The Dripping Faucet as a Model Chaotic System, Santa Cruz: Aerial Press.
Schneirla, T. C. (1971). Army Ants: A Study in Social Organization, H. Topoff (Ed.), San Francisco: Freeman.
Skaife, S. H. (1955). The Argentine Ant (Iridomyrmex humilis Mayr). Trans. R. Soc. South Afr. 34, 355–377.
Solé, R. V., O. Miramontes and B. C. Goodwin (1993). Oscillations and chaos in ant societies. J. Theor. Biol. 161, 343–357.
Takens, F. (1984). On the numerical determination of the dimension of an attractor. Lect. Notes in Math. 1125, 99–115.
Theiler, J. (1990). Statistical precision of dimension estimators. Phys. Rev. A 41, 3038–3051.
Theiler, J., S. Eubank, A. Longtin, B. Galdrikian and J. D. Farmer (1992). Testing for nonlinearity in time series: The method of surrogate data. Physica D 58, 77–92.
Theraulaz, G., E. Bonabeau and J. L. Deneubourg (1998). The origin of nest complexity in social insects. Complexity 3, 15–25.
Theraulaz, G., E. Bonabeau and J. L. Deneubourg (1999). The mechanisms and rules of coordinated building in social insects, in Information Processing in Social Insects, C. Detrain, J. L. Deneubourg and J. Pasteels (Eds), Basel: Birkhauser Verlag, pp. 309–330.
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Theraulaz, G., Bonabeau, E., Sauwens, C. et al. Model of droplet dynamics in the Argentine ant Linepithema humile (Mayr). Bull. Math. Biol. 63, 1079–1093 (2001). https://doi.org/10.1006/bulm.2001.0260
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DOI: https://doi.org/10.1006/bulm.2001.0260