Rare Periodic and Chaotic Attractors in Three-times Iterated Ikeda Map
Abstracts of 16th International Conference on Mathematical Modelling and Analysis (MMA2011) 2011
Aleksejs Klokovs, Mihails Zakrževskis

A new approach for the global bifurcation analysis, based on the ideas of Poincare, Birkho_ and Andronov, of nonlinear systems, described by discrete equations, is under consideration. The main idea of the approach is a concept of complete bifurcation groups and periodic branch continuation along stable and unstable solutions, named by one of the authors as a method of complete bifurcation groups (MCBG) [1; 2; 3; 4]. Rare attractors in di_erence nonlinear models, e.g. [5], can be found using the same approaches as for nonlinear ODE [4]. As examples we discuss using the method of complete bifurcation group for three-times iterated Ikeda map. The main results are presented by complete bifurcation diagrams for variable parameter b of the system. We have found di_erent new rare regular and chaotic attractors and some other new nonlinear phenomena such as cluster of submerged subharmonic isles, fully unstable subharmonic isle and multiplicity of chaotic attractor and usual of period-1 attractor. It is shown, that the parameter b of the three-times iterated Ikeda map is su_cient for global topology of the steady- state solutions of the system. All results were obtained numerically, using software SPRING [2], created in Riga Technical University.


Keywords
nonlinear discrete model, complete bifurcation analysis, method of complete bifurcation groups, rare attractors, unstable periodic infinitium, chaos, domains of attraction

Klokovs, A., Zakrževskis, M. Rare Periodic and Chaotic Attractors in Three-times Iterated Ikeda Map. In: Abstracts of 16th International Conference on Mathematical Modelling and Analysis (MMA2011), Latvia, Sigulda, 25-28 May, 2011. Rīga: University of Latvia, 2011, pp.73-73. ISBN 9789984453514.

Publication language
English (en)
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