Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells Model  

作　　者：Suqi Ma S. J. Hogan Suqi Ma;S. J. Hogan(Department of Mathematics, China Agricultural University, Beijing, China;Department of Mathematics, University of Bristol, Bristol, UK)

机构地区：[1]Department of Mathematics, China Agricultural University, Beijing, China [2]Department of Mathematics, University of Bristol, Bristol, UK

出　　处：《International Journal of Modern Nonlinear Theory and Application》2024年第2期11-28,共18页现代非线性理论与应用（英文）

摘　　要：The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.

关 键 词：Generalized Hopf Bifurcation DDE-Biftool Software Norm Form 

分 类 号：O17[理学—数学]