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Stability and bifurcation in a gene regulatory network model with delay
Author(s) -
Wang Z.,
Liu Z.,
Yuan R.
Publication year - 2012
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100079
Subject(s) - center manifold , hopf bifurcation , transcendental equation , bifurcation , mathematics , stability (learning theory) , saddle node bifurcation , biological applications of bifurcation theory , pitchfork bifurcation , transcritical bifurcation , transcendental number , bifurcation diagram , gene regulatory network , mathematical analysis , control theory (sociology) , numerical analysis , physics , computer science , gene , nonlinear system , gene expression , biology , biochemistry , control (management) , quantum mechanics , machine learning , artificial intelligence
A delayed gene regulatory network model with positive and negative feedbacks is considered. We investigate the stability of the positive equilibrium and the existence of Hopf bifurcation of the model by analyzing the associated characteristic transcendental equation. Applying the normal form theory and center manifold theorem, we consider the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions. An example is given and numerical simulations are performed to illustrate the obtained results.