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Mathematical Modeling of Condensing on Metric Spaces

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Abstract (2. Language): 
This work aims to present an energy based model of the collective dynamics where local interactions between particles of a collection causes all particles to reorganize in new positions. The self-organizing phenomenon involved by singular local moves of individual particles leads to condensing. This model is analyzed on metric spaces, simulated on a finite and in a continuous Euclidean subsets.
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REFERENCES

References: 

[1] P. Babak, G. Magnússon, , and S. Th. Sigurdsson. Dynamics of group formation in
collective motion of organisms. Mathematical Medicine and Biology, 21(4):269–292,
2004.
[2] S. N. Beshers and J. H. Fewell. Models of division of labor in social insects. Annual
Review of Entomology, 46(1):413–440, 2001.
[3] B. Birnir. An ODE Model of the Motion of Pelagic Fish. Journal of Statistical Physics,
128(1–2):535–568, 2007.
[4] C. M. Breder. Equations descriptive of fish schools and other animal aggregations. Ecol-
ogy, 35(3):361–370, 1954.
[5] F. Cucker and S. Smale. Emergent Behavior in Flocks. IEEE Transactions on Automatic
Control, 52(5):852–862, 2007.
[6] S. A. Frank. George Price’s contributions to evolutionary genetics. Journal of Theoretical
Biology, 175(3):373–388, 1995.
[7] S. A. Frank. The Price equation, Fisher’s fundamental theorem, kin selection, and causal
analysis. Evolution, 51(6):1712–1729, 1997.
[8] V. Gazi, Y. S. Hanay B. Fidan, and M. I. Köksal. Aggregation, Foraging, and Formation
Control of Swarms with Non-Holonomic Agents Using Potential Functions and Sliding
Mode Techniques. Turkish Journal of Electrical Engineering & Computer Sciences,
15(2):149–168, 2007.
[9] M. Gordon. The organization of work in social insect colonies. Nature, 380(6570):121–
124, 1996.
[10] M. J. Greene and D. M. Gordon. How patrollers set foraging direction in harvester ants.
The American Naturalist, 170(6):943–948, 2007.
REFERENCES 188
[11] R. Hegselmann and U. Krause. Opinion dynamics and bounded confidence models,
analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3):1–33,
2002.
[12] R. Hegselmann and U. Krause. Truth and cognitive division of labour: first steps towards
a computer aided social epistemology. Journal of Artificial Societies and Social
Simulation, 9(3):10, 2006.
[13] G. R. Price. Selection and covariance. Nature, 227(5257):520–521, 1970.
[14] G. R. Price. Extension of covariance selection mathematics. Annals of Human Genetics,
35(4):485–490, 1972.

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