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Offset parameter cancellation produces countless coexisting attractors.

Chunbiao Li1, Tengfei Lei2, Zuohua Liu3

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

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Summary
This summary is machine-generated.

This study reveals a novel mechanism for generating numerous coexisting attractors in dynamical systems. This finding introduces a new regime of multistability, explaining the origin and arrangement of these attractors.

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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • System variable averages dictate attractor positions.
  • Offset parameters can be eliminated, leaving initial conditions as the sole determinant of attractor location.
  • Parameter-dominated offset control leads to initial condition-defined coexisting attractors.

Purpose of the Study:

  • To disclose a special mechanism for generating countless coexisting attractors.
  • To reveal a new regime of multistability.
  • To explain the origin and arrangement of numerous coexisting attractors.

Main Methods:

  • Analysis of system variable dynamics.
  • Algebraic manipulation of offset parameters.
  • Investigation of initial condition influence on attractor positioning.

Main Results:

  • A novel mechanism for generating countless coexisting attractors has been identified.
  • A new regime of multistability has been discovered.
  • The birth and arrangement of numerous coexisting attractors are explained.

Conclusions:

  • The study successfully demonstrates a method for creating a vast number of coexisting attractors.
  • The newly revealed multistability regime provides a framework for understanding complex dynamical behaviors.
  • This work offers new insights into the control and prediction of system dynamics.