Modeling the pursuit in natural systems: A relaxed oscillation approach

We provide families of dynamical systems that model a wide range of cyclic pursuit mechanisms present in many organizations, which include the immune system, food chains and financial markets. A basic characteristic under study is the asymptotic behavior of the individual pursue of a system particle, cell or individual, to neighborhood particles. Relaxation oscillations are included in the systems in order to analyze different asymptotic scenarios. Several simulations will be presented and discussed that fit within the pursuit feature.