Stability and chaos analysis of a novel swarm dynamics with applications to multi-agent systems

This paper presents a novel swarm dynamics and illustrates its applications in automated multi-agent systems. The motion of the particles of the swarm in a particular landscape is governed by an attractant–repellent profile, which has an intimate linkage with the distance separating the particles. Following standard stability and chaos analysis procedures, it is demonstrated that the dynamics indeed simulates a swarm. We adopt a Lyapunov-function based stability and chaos analysis procedure to this effect. The parameterized conditions for which the dynamics exhibits chaotic characteristics are also investigated. Finally, the swarming dynamics is applied to a practical problem, thus elucidating how the proposition can be of use in a real-life situation. Since the dynamics rests on the values of certain parameters, we can control the areas in which we want to use the dynamics by controlling these parameters. The proposed dynamics will be shown to produce convergent, limit cyclic and chaotic behavior. This swarming dynamics can therefore be put to myriad uses depending on the application that is required.