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Related Experiment Video

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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Published on: September 23, 2025

Constructing an autonomous system with infinitely many chaotic attractors.

Xu Zhang¹, Guanrong Chen²

¹Department of Mathematics, Shandong University, Weihai 264209, Shandong, China.

Chaos (Woodbury, N.Y.)

|August 3, 2017

Summary

Researchers developed a new method to create chaotic systems with infinite chaotic attractors, unlike classical systems. This breakthrough applies to Lorenz-type and Rössler-type systems, even in fractional-order settings.

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Area of Science:

Nonlinear Dynamics and Chaos Theory
Mathematical Physics

Background:

Classical chaotic systems, like the Lorenz and Chua systems, typically exhibit a finite number of chaotic attractors.
Understanding and controlling chaotic behavior is crucial in various scientific and engineering fields.

Purpose of the Study:

To develop a novel and effective method for constructing autonomous systems with infinitely many chaotic attractors.
To demonstrate the applicability of this method to well-known chaotic system types.

Main Methods:

Development of a general method for generating lower-dimensional autonomous systems.
Application of bifurcation analysis to confirm the existence of infinite chaotic attractors.
Extension of the proposed method to fractional-order systems.

Main Results:

Successfully constructed Lorenz-type and Rössler-type systems exhibiting infinitely many chaotic attractors.
Demonstrated the effectiveness and simplicity of the developed construction method.
Showcased the adaptability of the method to fractional-order dynamics.

Conclusions:

The proposed method offers a significant advancement in the study of chaotic systems by enabling the creation of systems with infinite chaotic attractors.
This work provides new tools for exploring complex dynamics and opens avenues for further research in both integer and fractional-order chaotic systems.