Doubling the coexisting attractors

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.