Global Hopf Bifurcation Analysis for a Delayed Nicholson's Blowflies Model with Constant Reproductive Supply

Abstract

We investigate the dynamics of a delayed Nicholson's blowflies equation incorporating a constant reproductive supply that influences both density-dependent competition and egg production. The existence and local stability of the positive equilibrium are characterized via the analysis of the associated implicit and characteristic equations. Both local and global Hopf bifurcations are examined to establish conditions for the emergence of periodic solutions. Analytical and numerical results show that increasing the reproductive supply can restore the stability of the positive equilibrium by increasing the critical delay for the onset of Hopf bifurcation, in parameter regimes where sustained oscillations would otherwise occur.

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BibTeX

@article{lopes2026global,
  title = {{Global Hopf Bifurcation Analysis for a Delayed Nicholson's Blowflies Model with Constant Reproductive Supply}},
  author = {Luís E. S. Lopes and Mohammed Elghandouri and Mostafa Adimy and Cláudia P Ferreira},
  journal = {International journal of bifurcation and chaos in applied sciences and engineering},
  year = {2026},
  month = oct,
  doi = {10.1142/s0218127427500180},
  url = {https://hal.science/hal-05521793v2},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Global Hopf Bifurcation Analysis for a Delayed Nicholson's Blowflies Model with Constant Reproductive Supply
AU  - Luís E. S. Lopes
AU  - Mohammed Elghandouri
AU  - Mostafa Adimy
AU  - Cláudia P Ferreira
PY  - 2026
DA  - 2026/10/21
JO  - International journal of bifurcation and chaos in applied sciences and engineering
DO  - 10.1142/s0218127427500180
UR  - https://hal.science/hal-05521793v2
AB  - We investigate the dynamics of a delayed Nicholson's blowflies equation incorporating a constant reproductive supply that influences both density-dependent competition and egg production. The existence and local stability of the positive equilibrium are characterized via the analysis of the associated implicit and characteristic equations. Both local and global Hopf bifurcations are examined to establish conditions for the emergence of periodic solutions. Analytical and numerical results show that increasing the reproductive supply can restore the stability of the positive equilibrium by increasing the critical delay for the onset of Hopf bifurcation, in parameter regimes where sustained oscillations would otherwise occur.
SN  - 0218-1274
SN  - 1793-6551
ER  -

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