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Ma, S.Q., Feng, Z.S. and Lu, Q.S. (2008) A Two Parameter Criteria for Delay Differential Equations. Discrete & Continuous Dynamical Systems-B, 9, 397-413.
https://doi.org/10.3934/dcdsb.2008.9.397

has been cited by the following article:

• TITLE: Hopf Bifurcation of a Gene-Protein Network Module with Reaction Diffusion and Delay Effects

  AUTHORS: Suqi Ma Ma

  KEYWORDS: Partial Functional Differential Equations, Hopf Bifurcation, Normal Form

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.10 No.3, July 14, 2021

  ABSTRACT: The infinite dimensional partial delay differential equation is set forth and delay difference state feedback control is considered to describe the cell cycle growth in eukaryotic cell cycles. Hopf bifurcation occurs as varying free parameters and time delay continuously and the multi-layer oscillation phenomena of the homogeneous steady state of a simple gene-protein network module is investigated. Normal form is derived based on normal formal analysis technique combined with center manifold theory, which is further to compute the bifurcating direction and the stability of bifurcation periodical solutions underlying Hopf bifurcation. Finally, the numerical simulation oscillation phenomena is in coincidence with the theoretical analysis results.