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Offset boosting in chaotic systems doubles coexisting attractors using an absolute-value function. This technique enables geometric growth and merging of attractors, creating pseudo-multi-scroll attractors for advanced dynamics research.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Chaotic systems exhibit complex behaviors with multiple coexisting attractors.
  • Attractor shifting is a key technique for controlling system dynamics.

Purpose of the Study:

  • To introduce and analyze the offset boosting technique for attractor manipulation in chaotic systems.
  • To demonstrate the potential for geometric growth and merging of attractors.

Main Methods:

  • Application of an absolute-value function to implement offset boosting.
  • Analysis of attractor doubling and polymerization.
  • Demonstration of nesting and merging capabilities across dimensions.

Main Results:

  • Offset boosting effectively doubles the number of coexisting attractors.
  • The offset booster acts as a parameter controlling inter-attractor distance.
  • Pseudo-multi-scroll attractors are generated through attractor polymerization.
  • Attractor doubling can be nested, leading to geometric expansion.
  • Diverse attractor coexistence regimes can be merged into integrated attractors.

Conclusions:

  • The offset boosting technique offers a novel method for generating complex attractor structures.
  • This approach allows for precise control over the number and arrangement of attractors.
  • The findings have implications for designing and controlling chaotic systems with tailored dynamics.