Open AccessReplication of period-doubling route to chaos in coupled systems with delay
Author(s) -
Mehmet Onur Fen,
Fatma Tokmak Fen
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202599f
Subject(s) - cascade , replication (statistics) , mathematics , period doubling bifurcation , sensitivity (control systems) , bounded function , interval (graph theory) , chaos (operating system) , period (music) , doubling time , computer science , nonlinear system , mathematical analysis , combinatorics , statistics , physics , bifurcation , quantum mechanics , electronic engineering , chemistry , computer security , chromatography , acoustics , engineering , biochemistry , in vitro
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.