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

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Authors

  • Suqi Ma Department of Mathematics, China Agricultural University, Beijing, China Author
  • Qishao Lu Department of Mechanics, Beihang University, Beijing, China Author
  • S.J. Hogan Department of Mathematics, University of Bristol, Bristol, U.K Author

DOI:

https://doi.org/10.5890/JAND.2025.06.002

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

[1] Ma, S.Q. (2021), Two-dimensional manifolds of controlled Chen system, International Journal of Bifurcation and Chaos, 31(05), Article ID: 2150122. https://doi.org/10.1142/S0218127421501224.

[2] Ma, S.Q. (2021), Two-dimensional manifolds of modified Chen system with time delay, International Journal of Bifurcation and Chaos, 31(09), p.2150174, https://doi.org/10.1142/S0218127421501741.

[3] Jia, M. (2014), Growing 2D manifold of discrete dynamical system based on foliation condition, Chinese Journal of Computational Physics, 31, 495-505.

[4] Li, H.M., Fan, Y.Y., Sun, H.Y., Zhang, J., and Jia, M. (2012), Growing two-dimensional manifold of nonlinear maps based on generalized foliation condition, Acta Physica Sinica (Chinese), 61, 29501-029501. https://doi.org/10.7498/61.029501.

[5] Krauskopf, B. and Osinga, H. (1999), Two-dimensional global manifolds of vector fields, Chaos, 9, 768-774. https://doi.org/10.1063/1.166450.

[6] Krauskopf, B. and Osinga, H. (1999), Global manifolds of vector fields: the general case.

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PublishedJune 2025

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How to Cite

Ma, S., Lu, Q., & Hogan, S. (2026). Two Dimensional Unstable Manifold in a Delay Model of Neutrophil Cells Model. Journal of Applied Nonlinear Dynamics, 14(2), 253-261. https://doi.org/10.5890/JAND.2025.06.002