Constructing multi-butterfly attractors based on Sprott C system via non-autonomous approaches

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Complex Systems

Background:

• The Sprott C system is a well-known chaotic system.
• Generating complex attractors like multi-butterfly attractors is an active research area.
• Hidden attractors, lacking equilibrium points, present unique analytical challenges.

Purpose of the Study:

• To propose novel pulse control methods for generating multi-butterfly attractors.
• To investigate the creation of both translational and nested hidden multi-butterfly attractors.
• To demonstrate the flexibility and tunability of the proposed methods.

Main Methods:

• Introducing bipolar and unipolar multilevel pulse signals to the Sprott C system.
• Transforming non-autonomous systems into autonomous systems by including time as a state variable.
• Analyzing systems with no equilibria, characteristic of hidden attractors.
• Providing a normalized circuit implementation for validation.

Main Results:

• Successfully generated translational multi-butterfly attractors with constant Lyapunov exponents.
• Achieved nested multi-butterfly attractors through the superposition of attractors with varying pulse amplitudes.
• Demonstrated that the number of butterflies can be controlled by adjusting pulse voltage sources.
• Confirmed the existence of hidden multi-butterfly attractors in the circuit implementation.

Conclusions:

• The proposed pulse control methods effectively generate multi-butterfly hidden attractors.
• The methods offer a flexible approach to control attractor complexity without altering nonlinear functions.
• The findings contribute to the understanding and application of complex dynamical systems.