Two Dimensional Unstable Manifold in a Delay Model of Neutrophil Cells Model

Suqi Ma$^1$; Qishao Lu$^2$; S.J. Hogan$^3$

Journal of Applied Nonlinear Dynamics

Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)

Two Dimensional Unstable Manifold in a Delay Model of Neutrophil Cells Model

Journal of Applied Nonlinear Dynamics 14(2) (2025) 253--261 | DOI:10.5890/JAND.2025.06.002

Suqi Ma$^1$, Qishao Lu$^2$, S.J. Hogan$^3$

$^1$ Department of Mathematics, China Agricultural University, Beijing, China

$^2$ Department of Mechanics, Beihang University, Beijing, China

$^3$ Department of Mathematics, University of Bristol, Bristol, U.K

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Abstract

The two dimensional unstable manifolds of delay neutrophil model are drawn as system loss its stability. The attractors are stable solutions and the unstable manifolds which are originated from the equilibrium solution form the neighborhood boundary of the related attractor. Under the parameter perturbation with periodical excitation, the two dimensional manifolds are also drawn since the system has stable attractor too. The two dimensional manifold is also obtained by periodical excitation via perturbation about its apoptosis rate. The observed phenomena usually illustrate the oscillation with multi-rhythm periodical solutions in neutrophil system.

References

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