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Complex emergent dynamics of anisotropic swarms: Convergence vs oscillation. (English) Zbl 1142.34346

Summary: This paper considers an anisotropic swarm model with a simple attraction and repulsion function. It is shown that the members of a reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size around the swarm center. Moreover, the swarm system is also completely stable, i.e., every solution converges to the set of equilibrium points of the system. These results are also valid for a class of non-reciprocal swarms under the detailed balance condition on coupling weights. For general non-reciprocal swarms, numerical simulations are worked out to demonstrate more complex oscillatory motions in the systems. The study provides further insight into the effect of the interaction pattern on the collective behavior of a swarm system.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37N25 Dynamical systems in biology
92D50 Animal behavior
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