Iterated function systems of logistic maps: synchronization and intermittency

作者：Abbasi Neda^*; Gharaei Masoumeh; Homburg Ale Jan

来源：Nonlinearity, 2018, 31(8): 3880-3913.

DOI：10.1088/1361-6544/aac637

• iterated function system
• logistic family
• synchronization
• intermittency

We discuss iterated function systems generated by finitely many logistic maps, with a focus on synchronization and intermittency. We provide sufficient conditions for synchronization, involving negative Lyapunov exponents and minimal dynamics. A number of results that clarify the scope of these conditions are included. We analyze a mechanism for intermittency that involves the full map x -> 4x(1 - x) as one of the generators of the iterated function system. For iterated function systems generated by x -> 2x(1 - x) and x -> 4x(1 - x) we prove the existence of a sigma-finite stationary measure.

• 出版日期2018-8