Collective motion of a class of social foraging swarms

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.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  Long Wang,et al.  Complex emergent dynamics of anisotropic swarms: Convergence vs oscillation , 2006 .

[3]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[4]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[5]  Kevin M. Passino,et al.  Stability analysis of swarms , 2003, IEEE Trans. Autom. Control..

[6]  Tianguang Chu,et al.  Self-organized motion in anisotropic swarms , 2003 .

[7]  K. Passino,et al.  A class of attractions/repulsion functions for stable swarm aggregations , 2004 .

[8]  Long Wang,et al.  Swarming behavior of multi-agent systems , 2004, math/0405405.

[9]  T. Vicsek,et al.  Collective behavior of interacting self-propelled particles , 2000, cond-mat/0611742.

[10]  W. Rappel,et al.  Self-organization in systems of self-propelled particles. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  T. Vicsek,et al.  Spontaneously ordered motion of self-propelled particles , 1997, cond-mat/0611741.

[12]  A. Ōkubo.  Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[13]  Wang Long,et al.  Swarm Dynamics of a Group of Mobile Autonomous Agents , 2005 .

[14]  K. Passino,et al.  A class of attraction/repulsion functions for stable swarm aggregations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[15]  Hayakawa,et al.  Collective motion in a system of motile elements. , 1996, Physical review letters.

[16]  K.M. Passino,et al.  Stability analysis of social foraging swarms , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  C. Breder.  Equations Descriptive of Fish Schools and Other Animal Aggregations , 1954 .

[18]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[19]  Ronald C. Arkin,et al.  An Behavior-based Robotics , 1998 .

[20]  Sarika Jalan,et al.  Self-organized and driven phase synchronization in coupled map networks , 2003 .

[21]  Long Wang,et al.  Coordinated collective motion in a motile particle group with a leader , 2005 .

[22]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..