Exploring chaotic dynamics by partition of bifurcation diagram

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.