A Nullclines Approach to the Study of 2D Artificial Network

Abstract

The system of two the first-order ordinary differential equations arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described in three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problem in 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 on what to do in any particular situation.