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Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity
Cristiane Stegemann1, Holokx A Albuquerque, Paulo C Rech
1Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil. cristianestegemann@yahoo.com.br
Chaos (Woodbury, N.Y.)
|July 2, 2010
Summary
This study explores parameter spaces in a modified Chua oscillator model. Results reveal periodic structures within chaotic regions, organized by period-adding cascades, suggesting these patterns represent the overall parameter space.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Electronic Circuit Analysis
Background:
- The Chua oscillator is a fundamental system for studying chaos.
- Traditional models use a piecewise-linear nonlinearity for the Chua diode.
- Investigating alternative nonlinear functions can reveal new dynamical behaviors.
Purpose of the Study:
- To analyze the parameter space of a modified Chua oscillator model.
- To replace the standard piecewise-linear nonlinearity with a cubic polynomial.
- To identify and characterize dynamical structures within the parameter space.
Main Methods:
- Investigated three independent two-dimensional cross sections of the three-dimensional parameter space.
- Utilized autonomous differential equations to model the modified Chua oscillator.
- Analyzed the resulting diagrams for periodic structures and chaotic regions.
Main Results:
- All analyzed two-dimensional parameter space cross sections exhibited periodic structures.
- These periodic structures were embedded within a large chaotic region.
- The periodic structures were observed to organize into period-adding cascades.
Conclusions:
- The identified periodic structures and period-adding cascades are a significant feature of this modified Chua oscillator model.
- The investigated two-dimensional cross sections appear representative of the overall three-dimensional parameter space within the studied range.
- This cubic polynomial nonlinearity offers a different route to complex dynamics in Chua oscillator models.
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