1994•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIERequires access

Control of trajectories of the kicked logistic map

Maurı́cio S. Baptista, Iberê Luiz Caldas

Abstract

The main topological changes of the logistic map attractors, caused by a sequence of periodic kicks, are reported. This procedure brings up a three-parameter kicked logistic map with distinct dynamic features. Thus, its parameter space structure exhibits highly interleaved sets with different attractors, and complex basins of attraction are created. Consequently, the logistic map attractors can be modified or suppressed by these perturbations. Furthermore, additional roads to chaos, and abrupt attractor changes are identified in the new bifurcation diagrams.

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Key concepts: Attractor, Logistic map, Bifurcation, Parameter space, Topology (electrical circuits), Mathematics, Computer science, Sequence (biology)