Stability and Bifurcation Analysis of a Two-Dimensional Gene Regulatory Network
Stability and bifurcation analysis of a two-dimensional gene regulatory network is studied based on the dynamical systems theory.Firstly,the conditions for the existence of the equi-librium points are given,then stability of the equilibrium points is investigated.Secondly,the condi-tions for codimension-one Hopf bifurcation,Saddle-node bifurcation and codimension-two Bogdanov-Takens bifurcation are analyzed respectively.Finally,the correctness of the theoretical analysis is verified by the codimension-one bifurcation diagrams,codimension-two bifurcation diagram and phase diagrams.
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