zbMATH — the first resource for mathematics

Collective motion of a class of social foraging swarms. (English) Zbl 1142.92347
Summary: This paper considers a class of social foraging swarms with a nutrient profile (or an attractant/repellent) and an attraction-repulsion coupling function, which is chosen to guarantee collision avoidance between individuals. The paper also studies non-identical interaction ability or efficiency among different swarm individuals for different profiles. The swarm behavior is a result of a balance between inter-individual interplays as well as the interplays of the swarm individuals (agents) with their environment. It is proved that the individuals of a quasi-reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size for different profiles. It is also shown that the swarm system is completely stable, that is, every solution converges to the set of equilibrium points of the system. Moreover, all the swarm individuals will converge to more favorable areas of the profile under certain conditions. For general non-reciprocal swarms, numerical simulations show that more complex self-organized rotation may occur in the swarms.

92D50 Animal behavior
37N25 Dynamical systems in biology
Full Text: DOI
[1] Breder, C.M., Equation descriptive of fish schools and other animal aggregations, Ecology, 35, 361-370, (1954)
[2] Arkin, R., Behavior-based robotics, (1998), MIT Press Cambridge
[3] Lawton, J.R.T.; Beard, R.W.; Young, B.J., A decentralized approach to formation maneuvers, IEEE trans robot automat, 19, 933-941, (2003)
[4] Okubo, A., Dynamical aspects of animal grouping: swarms, schools, flocks, and herds, Adv biophys, 22, 1-94, (1986)
[5] 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, 675, 1226-1229, (1995)
[6] Shimoyama, N.; Sugawa, K.; Mizuguchi, T.; Hayakawa, Y.; Sano, M., Collective motion in a system of motile elements, Phys rev lett, 76, 3870-3873, (1996)
[7] Czirok, A.; Stanley, H.E.; Vicsek, T., Spontaneously ordered motion of self-propelled particles, J phys A: math gen, 30, 1375-1385, (1997)
[8] Toner, J.; Tu, Y., Flocks, herds, and schools: a quantitative theory of flocking, Phys rev E, 58, 4828-4858, (1998)
[9] Czirok, A.; Vicsek, T., Collective behavior of interacting self-propelled particles, Physica A, 281, 17-29, (2000)
[10] Levine, H.; Rappel, W.J., Self-organization in systems of self-propelled particles, Phys rev E, 63, 017101-1-017101-4, (2001)
[11] Gazi, V.; Passino, K.M., A class of attraction/repulsion functions for stable swarm aggregations, Proc IEEE conf decision contr, 2842-2847, (2002)
[12] Amritkar, R.E.; Jalan, S., Self-organized and driven phase synchronization in coupled map networks, Physica A, 321, 220-225, (2003) · Zbl 1020.37011
[13] Mu, S.; Chu, T.; Wang, L., Coordinated collective motion in a motile particle group with a leader, Physica A, 351, 211-226, (2005)
[14] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous members using nearest neighbor rules, IEEE trans automat contr, 48, 988-1001, (2003) · Zbl 1364.93514
[15] Gazi, V.; Passino, K.M., Stability analysis of swarm, IEEE trans automat contr, 48, 692-697, (2003) · Zbl 1365.92143
[16] Chu, T.; Wang, L.; Chen, T., Self-organized motion in anisotropic swarms, J contr theor appl, 1, 77-81, (2003)
[17] Chu, T.; Wang, L.; Chen, T.; Mu, S., Complex emergent dynamics of anisotropic swarms: convergence vs oscillation, Chaos, solitons & fractals, 30, 875-885, (2006) · Zbl 1142.34346
[18] Gazi, V.; Passino, K.M., Stability analysis of social foraging swarms, IEEE trans syst, man cybernet, part B: cybernetics, 34, 539-557, (2004)
[19] Shi, H.; Wang, L.; Chu, T., Swarm behavior of multi-agent systems, J contr theor appl, 4, 313-318, (2004)
[20] Liu, B.; Chu, T.; Wang, L.; Wang, Z.F., Swarm dynamics of a group of mobile autonomous agents, Chin phys lett, 22, 254-257, (2005)
[21] Khalil, H., Nonlinear system, (1996), Prentice Hall Inc. Upper Saddle River
[22] Horn, R.A.; Johnson, C.R., Matrix analysis, (1900), Cambridge University Press Cambridge
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.