Abstract
We study here a recently proposed theme of one group chasing another, called “group chase and escape”. Rather rich and complex behavior such as self-organized structures can arise from a model with simple rules. We discuss models with various cases of different speeds between the two groups, search ranges, and motion fluctuations.
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References
Isaacs, R.: Differential Games. John Wiley & Sons, New York (1965)
Basar, T., Olsder, G.: Dynamic Noncooperative Game Theory. Society for Industrial and Applied Mathematics, Philadelphia (1999)
Nahin, P.J.: Chases and Escapes: The mathmatics of pursuit and evasion. Princeton University Press, Princeton (2007)
Krapivsky, P.L., Redner, S.: Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions. J. Phys. A: Math Gen. 29, 5347 (1996)
Oshanin, G., Vasilyev, O., Krapivsky, P.L., Klafter, J.: Survival of an evasive prey. Proc. Nat. Acad. Sci. 106, 13696 (2009)
Hespanha, J.P., Kim, H.J., Sastry, S.: Multiple-Aagent Probabilistic Pursuit-Evasion Games. In: Proc. 38th Conference on Decision and Control, p. 2432 (1999)
Vidal, R., Shakernia, O., Kim, J.H., Shim, D.H., Sastry, S.: Multiple-Aagent Probabilistic Pursuit-Evasion Games with Unmanned Ground and Aerial Vehicles. IEEE Trans. Robotics and Automation 18, 662 (2002)
Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel Type of Phase Transition in a System of Self-Driven Particles. Phys. Rev. Lett. 75, 1226 (1995)
Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407, 487 (2000)
Romanczuk, P., Couzin, I.D., Schimansky-Geier, L.: Collective Motion due to Individual Escape and Pursuit Response. Phys. Rev. Lett. 102, 010602 (2009)
Kamimura, A., Ohira, T.: Group Chase and Escape. New J. Phys. 12, 053013 (2010)
Rogers, D.: Crawling Neutrophil Chasing a Bacterium (1950), http://www.biochemweb.org/neutrophil.shtml
Szor, P.: The art of computer virus research and defense. Addison Wesley Publishing Company, Upper Saddle River (2005)
Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259 (1996)
de Gennes, P.G.: Granular matter: a tentative view. Rev. Mod. Phys. 71, S374 (1999)
Kadanoff, L.P.: Built upon sand: Theoretical ideas inspired by granular flows. Rev. Mod. Phys. 71, 435 (1999)
Wolf, D.E., Schreckenberg, M., Bachem, A.: Traffic and Granular Flow. World Scientific, Singapore (1996)
Sugiyama, Y., Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S., Yukawa, S.: Traffic jams without bottlenecks - experimental evidence for the physical mechanism of the formation of a jam. New J. Phys. 10, 033001 (2008)
Alberts, B., Johnson, A., Walter, P., Lewis, J., Raff, M., Roberts, K.: Molecular Biology of the Cell, 5th edn. Garland Publishing, New York (2008)
MacDonald, C., Gibbs, J.: 1969 Concerning the kinetics of polypeptide synthesis on polyribosomes. Biopolymers 7, 707 (1969)
Matsumoto, S., Ito, N.: Dynamical Approach to Jam Phenomenon of Ribosomes. The Mathematical Society of Traffic Flow 15 (2009) (Japanese)
Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford (1999)
Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision - working in animal groups on the move. Nature 433, 513 (2005)
Glass, L., Mackey, M.C.: From Clocks to Chaos: The Rhythms of Life. Princeton University Press, Princeton (1988)
Ohira, T., Yamane, T.: Delayed Stochastic Systems. Phys. Rev. E 61, 1247 (2000)
Balachandran, B., Kalmar-Nagy, T., Gilsinn, D.E.: Delay Differential Equations: Recent Advances and New Directions. Springer, New York (2009)
Mackey, M.C., Glass, L.: Oscillation and Chaos in Physiological Control Systems. Science 197, 287 (1977)
Ohira, T., Milton, J.G.: Delayed Random walks. Phys. Rev. E 52, 3277 (1995)
Milton, J.G., Townsend, J.L., King, M.A., Ohira, T.: Balancing with positive feedback: the case for discontinuous control. Phil. Trans. Roy. Soc. A 367, 1181 (2009)
Milton, J.G., Cabrera, J.L., Ohira, T., Tajima, S., Tonosaki, Y., Eurich, C.W., Campbell, S.A.: The time delayed inverted pendulum: Implications for human balance control. Chaos 19, 026110 (2009)
Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E. 51, 1035 (1995)
Nakanishi, K., Itoh, K., Igarashi, Y., Bando, M.: Solvable optimal velocity models and asymptotic trajectory. Phys. Rev. E. 55, 6519 (1997)
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Kamimura, A., Matsumoto, S., Ito, N., Ohira, T. (2010). Chase and Escape in Groups. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_62
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DOI: https://doi.org/10.1007/978-3-642-15979-4_62
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