Editing Swarm behaviour (section)

====Self-propelled particles====
{{Main|Self-propelled particles}}
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|video1=[http://phet.colorado.edu/sims/self-driven-particle-model/self-driven-particle-model_en.jar SPP model interactive simulation]<ref>[http://www.colorado.edu/physics/pion/srr/particles/ Self driven particle model] {{webarchive|url=https://web.archive.org/web/20121014155808/http://www.colorado.edu/physics/pion/srr/particles/ |date=2012-10-14}} Interactive simulations, 2005, University of Colorado. Retrieved 10 April 2011.</ref><br/>– needs Java
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The concept of [[self-propelled particles]] (SPP) was introduced in 1995 by [[Tamás Vicsek]] ''et al.''<ref name="Vicsek1995">{{cite journal |vauthors= Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O |author-link= Vicsek T |year= 1995 |title= Novel type of phase transition in a system of self-driven particles |journal=[[Physical Review Letters]] |volume= 75 |issue= 6 |pages= 1226–1229 |doi= 10.1103/PhysRevLett.75.1226 |bibcode=1995PhRvL..75.1226V |arxiv= cond-mat/0611743 |pmid= 10060237|s2cid= 15918052 }}</ref> as a special case of the boids model introduced in 1986 by Reynolds.<ref name="Reynolds"/> An SPP swarm is modelled by a collection of particles that move with a constant speed and respond to random perturbations by adopting at each time increment the average direction of motion of the other particles in their local neighbourhood.<ref>{{cite journal |vauthors=Czirók A, Vicsek T |year= 2006 |title= Collective behavior of interacting self-propelled particles |journal= Physica A |volume= 281 |issue= 1–4 |pages= 17–29 |doi= 10.1016/S0378-4371(00)00013-3 |arxiv= cond-mat/0611742 |bibcode= 2000PhyA..281...17C|s2cid= 14211016 }}</ref>

Simulations demonstrate that a suitable "nearest neighbour rule" eventually results in all the particles swarming together, or moving in the same direction. This emerges, even though there is no centralized coordination, and even though the neighbours for each particle constantly change over time.<ref name="Vicsek1995"/> SPP models predict that swarming animals share certain properties at the group level, regardless of the type of animals in the swarm.<ref name="Buhl et al">{{cite journal |vauthors= Buhl J, ((Sumpter DJT)), Couzin D, Hale JJ, Despland E, Miller ER, Simpson SJ |display-authors= etal |year= 2006 |title= From disorder to order in marching locusts |url= http://webscript.princeton.edu/~icouzin/website/wp-content/plugins/bib2html/data/papers/buhl06.pdf |journal= Science |volume= 312 |issue= 5778 |pages= 1402–1406 |doi= 10.1126/science.1125142 |pmid= 16741126 |bibcode= 2006Sci...312.1402B |s2cid= 359329 |access-date= 2011-04-13 |archive-url= https://web.archive.org/web/20110929220754/http://webscript.princeton.edu/~icouzin/website/wp-content/plugins/bib2html/data/papers/buhl06.pdf |archive-date= 2011-09-29 |url-status= dead}}</ref> Swarming systems give rise to [[emergent behaviour]]s which occur at many different scales, some of which are both universal and robust. It has become a challenge in theoretical physics to find minimal statistical models that capture these behaviours.<ref>{{cite journal |vauthors= Toner J, Tu Y, Ramaswamy S |year= 2005 |title= Hydrodynamics and phases of flocks |url= http://eprints.iisc.ernet.in/3397/1/A89.pdf |journal= Annals of Physics |volume= 318 |issue= 1 |pages= 170–244 |bibcode= 2005AnPhy.318..170T |doi= 10.1016/j.aop.2005.04.011 |access-date= 13 April 2011 |archive-date= 18 July 2011 |archive-url= https://web.archive.org/web/20110718172510/http://eprints.iisc.ernet.in/3397/1/A89.pdf |url-status= dead }}</ref><ref name="Bertin et al">{{cite journal |last1= Bertin |first1= E |last2= Droz |last3= Grégoire |first3= G |year= 2009 |title= Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis |arxiv= 0907.4688 |journal= J. Phys. A |volume= 42 |issue= 44 |page= 445001 |doi= 10.1088/1751-8113/42/44/445001 |bibcode= 2009JPhA...42R5001B|s2cid= 17686543 }}</ref>