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In this study, replication of a period-doubling cascade in coupled systemswith delay is rigorously proved under certain assumptions, which guarantee theexistence of bounded solutions and replication of sensitivity. A noveldefinition for replication of sensitivity is utilized, in which the proximityof solutions is considered in an interval instead of a single point. Exampleswith simulations supporting the theoretical results concerning sensitivity andperiod-doubling cascade are provided.

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