Abstract
A swarming model is a model that describes the behavior of the social aggregation of a large group of animals or the community of humans. In this work, the swarming model that includes the short-range repulsion and long-range attraction with the presence of time delay is investigated. Moreover, the convergence to a consensus representing dispersion and cohesion properties is proved by using the Lyapunov functional approach. Finally, numerical results are provided to demonstrate the effect of time delay on the motion of the group of agents.
Highlights
The study of the behavior of interacting agents in groups of animals has gained increasing interest in various fields such as biology, engineering, mathematics
See, e.g., [1, 3, 4, 10, 11, 14, 16]. In connection with these swarming models, it is essential to mention that the continuous models are developed through partial differential equations (PDEs) that describes the evolution of the particles’ density in the systems composed of a large number of interacting agents such as cell, molecular organism, or chemo-taxis with high drift effect; see [13, 21]
2.3 The second-order model we focus on the swarming model which includes rules for orientation
Summary
The study of the behavior of interacting agents in groups of animals has gained increasing interest in various fields such as biology, engineering, mathematics (see [2, 8, 12, 15, 20]). In the first-order model, time-delays are included in the agents’ position, while in the second-order model, agents adapt their velocity relative to other agents’ velocities with communication delay Based on these two models, the emergence of the swarm into the pattern formation is theoretically and numerically investigated. The stability of swarming corresponding to dispersion and cohesion properties are investigated These properties are related to attraction and repulsion parameters (Ca, Cr, la, lr) in Morse potential function. We present results of numerical experiments to validate some aspects of theoretical findings and demonstrate the stability of swarms in two dimensions For this purpose, we consider the following four test-cases: Case I: Ca > Cr and la > lr Pattern configuration is formed and each agent moves with the same velocity
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