Cyclic pursuit problems in the two dimensional sphere

• We consider generalized pursuit models to investigate the asymptotic behavior in the two dimensional sphere.
• All cyclic pursuing particles tend to a planar circumference whose radius depends on the followed curve.
• All classical pursuing particles tend to a fixed point which depends on the initial positions of the whole set.

In this paper we consider several generalized pursuit models in order to investigate computationally and analytically the asymptotic behavior of a system of n   particles moving in the two dimensional sphere. We will consider two scenarios of pursuit, the first one given by the Limit cyclic pursuit with subcases given by using variable or constant speed. This scenario corresponds to a system of particles where one of them follows a trajectory given by a fixed curve and it is followed cyclically by a system of n-1n-1 particles using the shortest path between them. The second one is considering a set of particles moving on a sphere under a symmetric or non symmetric cyclic pursuit mechanism. The analysis will be presented with several simulations.