Replication of Period-Doubling Route to Chaos in Coupled Systems with Delay

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Fen M. O., FEN F.

FILOMAT, cilt.36, sa.2, ss.599-613, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2202599f
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.599-613
  • Anahtar Kelimeler: replication of chaos, period-doubling cascade, sensitivity, systems with delay, unidirectional coupling, DIFFERENTIAL-EQUATIONS, SYNCHRONIZATION, DYNAMICS
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, replication of a period-doubling cascade in coupled systems with delay is rigorously proved under certain assumptions, which guarantee the existence of bounded solutions and replication of sensitivity. A novel definition for replication of sensitivity is utilized, in which the proximity of solutions is considered in an interval instead of a single point. Examples with simulations supporting the theoretical results concerning sensitivity and period-doubling cascade are provided.