Delay-Induced Stability Transitions and Emergent Population Cycles in a Generalized Ecological Food Chain
Mathematics, cilt.14, sa.14, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 14
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14142530
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: ecological stability, equilibrium point, Hopf bifurcation, population cycles, sensitivity analysis, time delay
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
This research explores the influence of delayed species interactions on the stability of ecological communities. A generalized food-chain framework is considered, consisting of plants, herbivores, carnivores, and apex predators. Consumer growth in the model depends on resource availability at earlier times rather than instantaneously. By applying delay differential equations, we demonstrate that increasing time delays can destabilize an initially stable equilibrium and give rise to sustained oscillatory dynamics through a Hopf bifurcation. The analysis shows that once the delay exceeds a critical value, the equilibrium loses stability and periodic population cycles emerge. To analyze these dynamic transitions, techniques such as linear stability analysis, center manifold reduction, and normal form theory are employed. The calculation of key bifurcation coefficients determines the nature of the bifurcation, indicating that stable limit cycles typically form beyond the critical delay point. These findings provide a theoretical basis for understanding population fluctuations in natural systems, where time delays are inevitably due to resource tracking or developmental lags. The framework explains how ecological cycles can be driven by delayed interactions without the need for outside environmental forcing. Also, the proposed research supports Life on Land, Life Below Water, and Climate Action, by helping to provide understanding of ecological dynamics.