We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.
KeywordsTwo-dimensional discrete maps Sarkovski ordering Lyapunov exponents multiple basins
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- Lauwerier H A 1986Two-dimensional iterative maps in (ed) A V HoldenChaos Google Scholar