Qualitative features of a NPZ-Model

Qualitative study of higher order non linear dynamical systems? is a rewarding experience and a great challenge. This reflective paper is an attempt to deeply analyze interaction features between nutrients, phytoplanktons and zooplanktons by building a so-called NPZ-Model. We used classical methods (of Lyapunov, Hopf, etc.) to examine existence, positivity, boundedness and stability of solutions. Our main contribution is the implementation of a meaningful space parameter that simultaneously guarantees instability of equilibria at the border and? stability of the internal equilibrium. In the case of internal equilibrium instability, we observed the emergence of limit cycle which means the existence of periodical solutions.