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Remarks on multiparameter mappings: controlled-parameter and threshold maps

1983; Elsevier BV; Volume: 63; Issue: 1 Linguagem: Inglês

10.1016/0025-5564(83)90050-0

1879-3134

Thomas D. Rogers,

Chaos control and synchronization

We study the bifurcation properties in some examples of families of one-dimensional mappings depending on several parameters. In the case of a controlled parameter, alternating bands of chaos may occur in the bifurcation diagram, a characteristic usually associated with two-dimensional maps. Two-parameter families of threshold mappings provide another example, and we state geometrical conditions for almost all trajectories to converge to the origin or, alternatively, for the persistence of trajectories on a positive subinterval on which chaos may occur.