Replication of Period-Doubling Route to Chaos in Coupled Systems with Delay
FILOMAT, vol.36, no.2, pp.599-613, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 36 Issue: 2
- Publication Date: 2022
- Doi Number: 10.2298/fil2202599f
- Journal Name: FILOMAT
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Page Numbers: pp.599-613
- Keywords: replication of chaos, period-doubling cascade, sensitivity, systems with delay, unidirectional coupling, DIFFERENTIAL-EQUATIONS, SYNCHRONIZATION, DYNAMICS
- Open Archive Collection: AVESIS Open Access Collection
- TED University Affiliated: Yes
Abstract
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.