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Generating self-organizing collective behavior using separation dynamics from experimental data
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10.1063/1.4737203
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Affiliations:
1 Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2 School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, China
3 School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
a) Deceased.
b) Electronic mail: xiaokeeie@gmail.com.
c) Electronic mail: michael.small@uwa.edu.au.
Chaos 22, 033113 (2012)
/content/aip/journal/chaos/22/3/10.1063/1.4737203
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/3/10.1063/1.4737203

## Figures

FIG. 1.

Attraction/repulsion and speed curves obtained from cubic spline interpolations of our retrieved statistics.19 The plots show change in separation (a)and speed (b) for the next time interval () as a function of average separation to neighbors of an individual i at time t, denoted . Sample time is 2 s.

FIG. 2.

Simulations with M = 15, , . Random initial orientations in (a), snapshot at t = 150. Initially aligned orientations in (b), snapshots at t = 150 and t = 500 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4737203.1] [URL: http://dx.doi.org/10.1063/1.4737203.2]10.1063/1.4737203.110.1063/1.4737203.2

FIG. 3.

Simulations with . M = 30, , and random initial orientations in (a), snapshot at t = 1000. M = 50, , and initially aligned orientations in (b), snapshot at t = 1000 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4737203.3] [URL: http://dx.doi.org/10.1063/1.4737203.4]10.1063/1.4737203.310.1063/1.4737203.4

FIG. 4.

Simulations with M = 50, , . Random initial orientations in (a), snapshot at t = 400. Initially aligned orientations in (b), snapshots at t = 400 and t = 1000 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4737203.5] [URL: http://dx.doi.org/10.1063/1.4737203.6]10.1063/1.4737203.510.1063/1.4737203.6

FIG. 5.

From order to uncertainty (semi-vortex): a simulation with M = 50, , , and initially aligned orientations, at t = 500 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4737203.7]10.1063/1.4737203.7

FIG. 6.

Simulations with M = 50, , . Divided initial orientations in (a), half the population pointing at 0 and the other half at , snapshots at t = 500 and t = 1200. Initially aligned orientations in (b), snapshot at t = 500 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4737203.8] [URL: http://dx.doi.org/10.1063/1.4737203.9]10.1063/1.4737203.810.1063/1.4737203.9

FIG. 7.

Rough sketches of behavior zones for different initial densities (radius ) and interacting neighbors (M); with a resolution of 46 × 46 parameter settings. All simulations had N = 100 and .

FIG. 8.

Averaged and values for 50 simulations of 1000 time intervals at different initial densities (radius ) and M = 50. Plots (a) and (c) correspond to random initial orientations, while (b) and (d) to aligned initial orientations. The transitions from a cohesive state to a vortex can be seen by the decrease of global direction , and increase of . The vertical lines correspond to the manual qualitative observations from Figure 7.

FIG. 9.

Time courses of and for three scenarios (M = 50): cohesive unit (random initial orientations, ), vortex (random initial orientations, ), and semi-vortex (aligned initial orientations, ). The time series were averaged over 50 simulations each.

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