Generation of multi-scroll attractors without equilibria via piecewise linear systems

Area of Science:

• Non-linear dynamics
• Chaos theory
• Dynamical systems

Background:

• Dynamical systems often exhibit equilibrium points, which represent stable or unstable states.
• Understanding systems without equilibria is crucial for modeling complex phenomena.
• Multiscroll attractors represent complex dynamical behaviors in certain systems.

Purpose of the Study:

• To introduce a new class of dynamical systems characterized by the absence of equilibria.
• To present a novel system possessing a multiscroll attractor.
• To demonstrate chaotic behavior in a simple, piecewise-linear dynamical system.

Main Methods:

• Development of a piecewise-linear dynamical system.
• Analysis of system stability.
• Application of the 0-1 Test for Chaos to confirm chaotic behavior.

Main Results:

• The proposed system is demonstrated to be simple and stable.
• The system exhibits a multiscroll attractor.
• Chaotic dynamics were confirmed using the 0-1 Test for Chaos.

Conclusions:

• A novel, simple, and stable piecewise-linear dynamical system without equilibria has been presented.
• The system successfully demonstrates a multiscroll attractor and chaotic behavior.
• This model provides a valuable tool for investigating analogous non-linear systems.