TIME-DELAY-INDUCED HOPF BIFURCATION IN A FRACTIONAL-ORDER ECOLOGICAL SYSTEM

ÇELİK KARAASLANLI C., Değerli K.

Communications in Mathematical Biology and Neuroscience, cilt.2026, 2026 (ESCI, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026
  • Basım Tarihi: 2026
  • Doi Numarası: 10.28919/cmbn/9725
  • Dergi Adı: Communications in Mathematical Biology and Neuroscience
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: bifurcation analysis, dynamical system, fractional calculus, numerical simulation, stability
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we investigate a fractional-order delayed dynamical system. Taking the time delay τ as the bifurcation parameter, we establish that the equilibrium is asymptotically stable for all τ < τ0, and a Hopf bifurcation occurs as τ passes through the critical value τ0 . We derive the characteristic equation and verify the transversality condition, which identifies the onset of oscillations and characterizes the stability of the emerging periodic solutions. Numerical experiments carried out in MATLAB with a predictor–corrector scheme support the analysis and illustrate the resulting oscillatory behavior.