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Analytical study of funnel type Rössler attractor.
An-Liang Cheng1, Yih-Yuh Chen1
1Department of Physics, National Taiwan University, Taipei 10617, Taiwan.
Chaos (Woodbury, N.Y.)
|August 3, 2017
Summary
We simplified chaotic Rössler attractor behavior using an approximate iteration scheme. This method reveals how parameter changes affect peak height and duration in chaotic dynamics.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Dynamical systems
Background:
- The Rössler attractor exhibits complex, chaotic behavior.
- Analyzing time-continuous chaotic systems can be challenging.
- Funnel type attractors present unique analytical difficulties.
Purpose of the Study:
- To simplify the analysis of chaotic trajectories in a funnel type Rössler attractor.
- To develop an approximate iteration scheme for describing chaotic dynamics.
- To facilitate the understanding of parameter-dependent variations in chaotic systems.
Main Methods:
- A suitable averaging method was employed.
- An approximate four-parameter surrogate iteration scheme was developed.
- The proposed scheme approximates the time-continuous chaotic behavior.
Main Results:
- The iteration scheme successfully describes the chaotic behavior.
- The method allows for easier observation of peak height and duration variations.
- Analytical results align well with numerical integration findings.
Conclusions:
- The approximate iteration scheme provides an effective simplification for analyzing Rössler attractors.
- This approach enhances the understanding of parameter tuning effects on chaotic dynamics.
- The method offers a valuable tool for studying complex dynamical systems.
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