ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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Numerical Explorations of the Ikeda Mapping Dynamics


George Osipenko

Laboratory of Nonlinear Analysis,
St. Petersburg State Polytechnic University


The Ikeda map occurs in the modeling of optical recording media (crystals). Under certain parameter values the Ikeda map exhibits highly complicated dynamical behavior. In particular, the Ikeda map can have infinitely many hyperbolic periodic orbits, which are located in a bounded part of the plane, and a strange attractor (the Ikeda attractor). The aim of the paper is to give an analysis of the topological structure of orbits by symbolic dynamics methods (the package ASIDS) and by methods of curves iteration (the package Line). Some possible modifications of the Ikeda mapping are considered.
An analysis of orbit behavior near fixed and periodic points and of bifurcations to chaos is presented.

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