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

作　　者：S. Q. Ma S. Q. Ma(Department of Mathematics, China Agricultural University, Beijing, China)

机构地区：[1]Department of Mathematics, China Agricultural University, Beijing, China

出　　处：《International Journal of Modern Nonlinear Theory and Application》2021年第3期91-105,共15页现代非线性理论与应用（英文）

摘　　要：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.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.

关 键 词：Partial Functional Differential Equations Hopf Bifurcation Normal Form 

分 类 号：O17[理学—数学]