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A Hidden Chaotic System with Multiple Attractors.

Xiefu Zhang1,2, Zean Tian1,3, Jian Li2

  • 1Institute of Advanced Optoelectronic Materials, Technology of School of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China.

Entropy (Basel, Switzerland)
|October 23, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel hidden chaotic system lacking equilibrium points. Analysis reveals diverse attractor behaviors and confirms its physical realizability, offering new insights into chaotic dynamics.

Keywords:
Spectral Entropycoexistence attractorselectronic circuithidden attractorsmultiple attractorstransition behavior

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Complex Systems Analysis

Background:

  • Chaotic systems are fundamental in understanding complex phenomena.
  • Systems without equilibrium points present unique analytical challenges.
  • Identifying and controlling chaotic behaviors are crucial for applications.

Purpose of the Study:

  • To introduce and analyze a novel hidden chaotic system without equilibrium points.
  • To explore the system's dynamical behaviors, including attractor coexistence and hyperchaos.
  • To validate the system's physical implementability.

Main Methods:

  • Numerical simulations using MATLAB R2018.
  • Analysis of Largest Lyapunov exponent, bifurcation diagrams, and phase portraits.
  • Application of Spectral Entropy for system state identification.
  • Physical implementation and verification.

Main Results:

  • Discovery of a hidden chaotic system with no equilibrium point.
  • Identification of seven distinct attractor types through parameter variation.
  • Observation of phenomena like coexisting attractors, controllability, and hyperchaotic behavior.
  • Successful physical implementation confirming system realizability.

Conclusions:

  • The proposed hidden chaotic system exhibits rich dynamics and unique characteristics.
  • Spectral Entropy provides an effective method for state identification.
  • The system's physical realizability opens avenues for practical applications in secure communication and signal processing.