Abstract
Research in biology is increasingly interested in discrete dynamical systems to simulate natural phenomena with simple models. But how to take into account their robustness? We illustrate this issue by considering the behaviour of a lattice-gas model with an alignment-favouring interaction rule. This model, which has been shown to display a phase transition between an ordered and a disordered phase, follows ergodic dynamics. We present a method based on the study of stability and robustness, and show that the organised phase may result in several different behaviours. We then observe that behaviours are influenced asymptotically by the definition of the cellular lattice.
Keywords
- Swarming behaviour
- lattice-gas cellular automata
- phase transitions
- robustness
- discretisation effects
- resonance effects
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References
Ermentrout, G.B., Edelstein-Keshet, L.: Cellular automata approaches to biological modeling. Journal of Theoretical Biology 160(1), 97–133 (1993)
Chevrier, V., Fatès, N.: How important are updating schemes in multi-agent systems? an illustration on a multi-turmite model. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 533–540 (2010)
Slotine, J., Li, W., et al.: Applied nonlinear control, vol. 66. Prentice hall, Englewood Cliffs (1991)
Grilo, C., Correia, L.: Effects of asynchronism on evolutionary games. Journal of Theoretical Biology 269(1), 109–122 (2011)
Bouré, O., Fatès, N., Chevrier, V.: Probing robustness of cellular automata through variations of asynchronous updating. Natural Computing 11(4), 553–564 (2012)
Vicsek, T., Zafeiris, A.: Collective motion. Physics Reports 517(3-4), 71–140 (2012)
Deutsch, A., Theraulaz, G., Vicsek, T.: Collective motion in biological systems. Interface Focus 2, 689–692 (2012)
Peruani, F., Ginelli, F., Bär, M., Chaté, H.: Polar vs. apolar alignment in systems of polar self-propelled particles. Journal of Physics: Conference Series 297(1), 012014 (2011)
Deutsch, A.: Orientation-induced pattern formation: Swarm dynamics in a lattice-gas automaton model. International Journal of Bifurcation and Chaos 6(9), 1735–1752 (1996)
Whitelam, S., Feng, E.H., Hagan, M.F., Geissler, P.L.: The role of collective motion in examples of coarsening and self-assembly. Soft Matter 5, 1251–1262 (2009)
Chopard, B., Ouared, R., Deutsch, A., Hatzikirou, H., Wolf-Gladrow, D.: Lattice-gas cellular automaton models for biology: From fluids to cells. Acta Biotheoretica 58, 329–340 (2010)
Hatzikirou, H., Brusch, L., Schaller, C., Simon, M., Deutsch, A.: Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion. Computers Mathematics with Applications 59(7), 2326–2339 (2010)
Helbing, D., Isobe, M., Nagatani, T., Takimoto, K.: Lattice gas simulation of experimentally studied evacuation dynamics. Physical Review E 67, 067101 (2003)
Lerner, A., Chrysanthou, Y., Lischinski, D.: Crowds by example. Computer Graphics Forum 26(3), 655–664 (2007)
Kennedy, J., Eberhart, R.C.: A discrete binary version of the particle swarm algorithm. Systems, Man, and Cybernetics 5, 4104–4108 (1997)
Leung, H., Kothari, R., Minai, A.A.: Phase transition in a swarm algorithm for self-organized construction. Physical Review E 68(4), 046111 (2003)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Sochet, O.: Novel type of phase transition in a system of self-driven particles. Physical Review Letters 75, 1226 (1995)
Deutsch, A.: Orientation-induced pattern formation: swarm dynamics in a lattice-gas automaton model. International Journal of Bifurcation and Chaos 6, 1735–1752 (1996)
Deutsch, A., Dormann, S.: Cellular Automaton Modeling of Biological Pattern Formation. Birkhauser Boston (2005)
Csahók, Z., Vicsek, T.: Lattice-gas model for collective biological motion. Physical Review E 52, 5297–5303 (1998)
Bussemaker, H.J., Deutsch, A., Geigant, E.: Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. Physical Review Letters 78(26), 5018–5021 (1997)
Peruani, F., Klauss, T., Deutsch, A., Voss-Boehme, A.: Traffic jams, gliders, and bands in the quest for collective motion of self-propelled particles. Physical Review Letters 106, 128101 (2011)
Manzo, F., Olivieri, E., Nardi, F., Scoppola, E.: On the essential features of metastability: Tunnelling time and critical configurations. Journal of Statistical Physics 115, 591–642 (2004)
Cirillo, E., Nardi, F., Spitoni, C.: Metastability for reversible probabilistic cellular automata with self-interaction. Journal of Statistical Physics 132, 431–471 (2008)
Bouré, O., Fatès, N., Chevrier, V.: A robustness approach to study metastable behaviours in a lattice-gas model of swarming, Tech. rep., LORIA – Inria Nancy Grand-Est – Université de Lorraine (2013)
Bouré, O., Fatès, N., Chevrier, V.: First steps on asynchronous lattice-gas models with an application to a swarming rule. Natural Computing (to appear)
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Bouré, O., Fatès, N., Chevrier, V. (2013). A Robustness Approach to Study Metastable Behaviours in a Lattice-Gas Model of Swarming. In: Kari, J., Kutrib, M., Malcher, A. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2013. Lecture Notes in Computer Science, vol 8155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40867-0_6
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DOI: https://doi.org/10.1007/978-3-642-40867-0_6
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