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A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis
1Electronic Engineering College, Heilongjiang University, Harbin 150080, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
A new method constructs quadratic polynomial chaotic maps for applications like secure communication. These maps satisfy chaos definitions and avoid hidden chaotic attractors, offering controlled chaotic time series amplitudes.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Nonlinear Dynamics
Background:
- Chaotic systems are crucial for secure communication and pseudorandom sequence generation.
- Existing construction methods rely on exhaustive search, particularly for systems with hidden chaotic attractors.
- A systematic construction theory for chaotic systems is lacking.
Purpose of the Study:
- To propose a general method for constructing quadratic polynomial chaotic maps.
- To ensure the constructed maps satisfy the Li-Yorke definition of chaos.
- To demonstrate control over chaotic time series amplitude and analyze attractor properties.
Main Methods:
- Developing a general construction method for quadratic polynomial chaotic maps.
- Analyzing the existence and stability of fixed points for the proposed maps.
- Verifying the Li-Yorke definition of chaos for the generated maps.
Main Results:
- A novel method for constructing quadratic polynomial chaotic maps is presented.
- The proposed maps exhibit chaotic behavior according to the Li-Yorke definition.
- Accurate control over the amplitude of chaotic time series is achieved.
- Analysis confirms that these quadratic polynomial maps do not possess hidden chaotic attractors.
Conclusions:
- The proposed method offers a systematic approach to constructing chaotic maps.
- The developed quadratic polynomial chaotic maps are suitable for practical applications requiring controlled chaos.
- The absence of hidden chaotic attractors simplifies their analysis and application.
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