A nullclines approach to the study of 2D artificial network

  • Felikss Sadirbajevs Institute of Mathematics and Computer Science, University of Latvia
Keywords: gene regulatory networks, phase portraits, bifurcations, critical points, attractors


The system of two the first order ordinary differential equa-tions arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described for three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problemin full generality. A number of propositions are stated and the proof is geometrical, avoiding complex analytic. Although not all the possible cases are considered, the instructions are given what to do in any particular situation.