A Nullclines Approach to the Study of 2D Artificial Network

Contemporary Mathematics 2019
Felix Sadyrbaev, Diana Ogorelova, Inna Samuilika

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 for 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 what to do in any particular situation.

Atslēgas vārdi
gene regulatory networks, phase portraits, bifurcations, critical points, attractors
DOI
10.37256/cm.11201976.1-11
Hipersaite
http://ojs.wiserpub.com/index.php/CM/article/view/cm.11201976.1-11

Sadyrbaev, F., Ogorelova, D., Samuilika, I. A Nullclines Approach to the Study of 2D Artificial Network. Contemporary Mathematics, 2019, Vol. 1, No. 1, 1.-11.lpp. ISSN 2705-1064. e-ISSN 2705-1056. Pieejams: doi:10.37256/cm.11201976.1-11

Publikācijas valoda
English (en)