Polarity balance for attractor self-reproducing.

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Complex Systems Analysis
• Engineering Applications in Circuits and Chemical Processes

Background:

• Nonlinear dynamical systems exhibit complex chaotic manifolds with unique geometric and physical properties.
• System attractors possess characteristics like granularity, orientation, and spatiotemporal distribution.
• Polarity balance is a critical factor influencing system solutions, including symmetrization, attractor merging, and self-reproduction.

Purpose of the Study:

• To investigate the role of polarity balance in controlling attractor distribution within nonlinear dynamical systems.
• To explore how absolute value and signum functions regulate polarity balance for attractor management.
• To understand the mechanism of attractor self-reproducing for constructing multistability.

Main Methods:

• Utilizing absolute value and signum functions to manage and control polarity balance.
• Investigating the switching dynamics of polarity balances to regulate attractor distribution.
• Analyzing the conditions and mechanisms for attractor self-reproducing and offset boosting.

Main Results:

• Demonstrated that polarity balance, regulated by specific functions, strictly controls attractor distribution.
• Identified attractor self-reproducing as a key regime for achieving desired multistability.
• Showcased the necessity of polarity controllers for restoring imbalanced polarity in attractor offset boosting.

Conclusions:

• Polarity balance is fundamental for the behavior and control of nonlinear dynamical systems.
• Attractor self-reproducing offers a viable pathway for engineering multistable systems.
• Effective polarity control is essential for manipulating attractor properties and achieving desired system outcomes.