Reference : Exploring chaotic dynamics by partition of bifurcation diagram
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Exploring chaotic dynamics by partition of bifurcation diagram
Changaival, Boonyarit mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Rosalie, Martin mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Proceeding of Workshop on Advance in Nonlinear Complex Systems and Applications (WANCSA)
Workshop on Advance in Nonlinear Complex Systems and Applications (WANCSA)
from 04-07-2017 to 05-07-2017
M. Aziz Alaoui
Cyrille Bertelle
Jie Liu
Damien Olivier
Le Havre
[en] Bifurcation Diagram ; Chaotic Dynamics ; First Return Map ; Rössler System ; Uniform Random Function
[en] Chaotic dynamical systems have been recently successfully used to replace uniform probability functions in several algorithms in optimization and machine learning. In this work, we propose a study on the use of bifurcation diagrams and first return map in the Rössler system for producing chaotic dynamics. Then, we plan to use these chaotic dynamic for optimization problem. With a bifurcation diagram we can also distinguish the periodic solutions apart from the chaotic solutions. By studying the chaotic solutions, we can then achieve a first return map which is a signature of the dynamical system and thoroughly study the complexity of the latter with a certain set of parameters. As a result, the partition in the bifurcation diagram is provided. From the first return maps, we are able to confirm the complexity of the dynamics in those partitions along with the transitions between them.
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