Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity

• Main Author: Stegemann C.*
• Publication Date: 2010
• Other Authors: Rech P.C.*, Albuquerque, Holokx Abreu
• Format: Article
• Language: eng
• Source: Repositório Institucional da Udesc
• dARK ID: ark:/33523/001300000vc85
• Download full: https://repositorio.udesc.br/handle/UDESC/9839

In this paper we investigate three two-dimensional parameter spaces of a three-parameter set of autonomous differential equations used to model the Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. It is made by using three independent two-dimensional cross sections of the three-dimensional parameter space generated by the model, which contains three parameters. We show that, independent of the parameter set considered in plots, all the diagrams present periodic structures embedded in a large chaotic region, and we also show that these structures organize themselves in period-adding cascades. We argue that these selected two-dimensional cross sections can be representative of the three-dimensional parameter space as a whole, in the range of parameters here investigated. © 2010 American Institute of Physics.