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Offset boosting in a discrete system.

Chunbiao Li1, Chenlong Yi2, Yongxin Li2

  • 1School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China.

Chaos (Woodbury, N.Y.)
|March 6, 2024
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Summary
This summary is machine-generated.

Offset boosting in discrete maps is achieved by preserving differentiation properties, enabling flexible multistability. This method, demonstrated in the Hénon map, offers new avenues for chaos regulation and attractor transportation in electronic engineering.

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Area of Science:

  • Chaos theory
  • Nonlinear dynamics
  • Electronic engineering

Background:

  • Offset boosting is crucial for chaos applications in electronic engineering.
  • Direct variable substitution in discrete maps can disrupt their inherent dynamics.
  • Discrete systems lack the variable differentiation dimension (DVD) found in continuous systems.

Purpose of the Study:

  • To achieve offset boosting in discrete maps while preserving their dynamics.
  • To explore flexible multistability, such as attractor self-reproducing and doubling.
  • To demonstrate a reliable method for offset boosting in discrete systems.

Main Methods:

  • Preserving the key property of differentiation of variable dimension (DVD) in discrete systems.
  • Implementing offset boosting through parameter or initial condition adjustments.
  • Utilizing a two-dimensional Hénon map as a case study for demonstration.

Main Results:

  • Offset boosting was successfully achieved in the Hénon map via parameter and initial condition manipulation.
  • The method preserves the essential dynamics of the discrete map.
  • Flexible multistability, including attractor self-reproducing and doubling, was realized.

Conclusions:

  • Offset boosting can be effectively implemented in discrete maps by preserving DVD.
  • This approach enables novel forms of multistability and offers new possibilities for chaos regulation.
  • Circuit experiments validated the reliability of the proposed offset boosting technique.