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Received: 2005-09-26

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.952-959


Modelling and stability analysis of emergent behavior of scalable swarm system

Author(s):  CHEN Shi-ming, FANG Hua-jing

Affiliation(s):  Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; more

Corresponding email(s):   c1977318@hotmail.com

Key Words:  Two-layer emergent model, Stability, Emergent behavior, Swarm

CHEN Shi-ming, FANG Hua-jing. Modelling and stability analysis of emergent behavior of scalable swarm system[J]. Journal of Zhejiang University Science A, 2006, 7(6): 952-959.

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%DOI 10.1631/jzus.2006.A0952

T1 - Modelling and stability analysis of emergent behavior of scalable swarm system
A1 - CHEN Shi-ming
A1 - FANG Hua-jing
J0 - Journal of Zhejiang University Science A
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SP - 952
EP - 959
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A0952

In this paper we propose a two-layer emergent model for scalable swarm system. The first layer describes the individual flocking behavior to the local goal position (the center of minimal circumcircle decided by the neighbors in the positive visual set of individuals) resulting from the individual motion to one or two farthest neighbors in its positive visual set; the second layer describes the emergent aggregating swarm behavior resulting from the individual motion to its local goal position. The scale of the swarm will not be limited because only local individual information is used for modelling in the two-layer topology. We study the stability properties of the swarm emergent behavior based on Lyapunov stability theory. Simulations showed that the swarm system can converge to goal regions while maintaining cohesiveness.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Aldana, M., Huepe, C., 2003. Phase transitions in self-driven many-particle systems and related non-equilibrium models: a network approach. Journal of Statistical Physics, 112(1/2):135-153.

[2] Breder, C.M., 1954. Equations descriptive of fish schools and other animal aggregations. Ecology, 35(3):361-370.

[3] Chen, S.M., Fang, H.J., 2005. Modeling and stability analysis of large-scale swarm. Control and Decision, 20:490-494.

[4] Chen, S.M., Fang, H.J., 2006. An improved cooperative tracking model used for large-scale foraging swarm. ACTA Automatica SINICA, in press.

[5] Chu, T., Wang, L., Chen, T., 2003. Self-organized motion in anisotropic swarms. Journal of Control Theory and Applications, 1:77-81.

[6] Couzin, I., Krause, J., James, R., 2002. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology, 218(1):1-11.

[7] Erdmann, U., Ebeling, W., 2003. Collective motion of Brownian particles with hydrodynamic interactions. Fluctuation and Noise Letters, 3(2):145-154.

[8] Gazi, V., Passino, K.M., 2003. Stability analysis of swarms. IEEE Transactions on Automatic Control, 48(4):692-697.

[9] Gazi, V., Passino, K.M., 2004. Stability analysis of social foraging swarms. IEEE Transactions on Systems, Man, and CyberneticsPart B: Cybernetics, 34(1):539-556.

[10] Ge, G.Y., Tang, J.X., 1996. Quick algorithm of circularity evaluation based on minimal circumcircle and maximal inscribed circle methods. Metrology and Measurement Technique, 23:11-12.

[11] Grunbaum, D., Okubo, A., 1994. Modeling social animal aggregations. Frontiers in Theoretical Biology, 100:296-325.

[12] Jadbabaie, A., Lin, J., Morse, A.S., 2003. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6):988-1001.

[13] Liu, Y.F., Passino, K.M., 2004. Stable social foraging swarms in a noisy environment. IEEE Transactions on Automatic Control, 49(1):30-44.

[14] Liu, B., Chu, T.G., Wang, L., Wang, Z.F., 2005. Swarm dynamics of a group of mobile autonomous agents. Chinese Physics Letters, 22(1):254-257 (in Chinese).

[15] Mogilner, A., Bent, L., Spiros, A., Edelstein-Keshet, L., 2003. Mutual interactions, potentials and individual distance in a social aggregation. Journal of Mathematical Biology, 47(4):353-389.

[16] Okubo, A., 1986. Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Advances in Biophysics, 22:1-94.

[17] Parrish, J., Viscido, S., Grunbaum, D., 2003. Self-organized fish schools: an examination of emergent properties. Biological Bulletin, 202:296-305.

[18] Shi, H., Wang, L., Chu, T., 2004. Swarming behavior of multi-agent systems. Journal of Control Theory and Applications, 4:313-318.

[19] Topaz, C., Bertozzi, A., 2004. Swarming patterns in a two-dimensional kinematic model for biological groups. SIAM Journal on Applied Mathematics, 65(1):152-174.

[20] Warburton, K., Lazarus, J., 1991. Tendency-distance models of social cohesion in animal groups. Journal of Theoretical Biology, 150:473-488.

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