Periodic offset boosting for attractor self-reproducing

Area of Science:

• Dynamical Systems and Chaos Theory
• Nonlinear Dynamics

Background:

• Multistability and attractor self-reproduction are complex phenomena in dynamical systems.
• Understanding the underlying mechanisms is crucial for controlling system behavior.

Purpose of the Study:

• To decode the special regime of multistability of attractor self-reproducing.
• To establish a universal law for attractor self-reproducing based on offset boosting.

Main Methods:

• Investigating attractor self-reproducing triggered by periodic initial condition-offset boosting.
• Analyzing the influence of position, size, and clone frequency on trigonometric function selection.
• Developing a universal law based on three sinusoidal quantity elements: initial phase, amplitude, and frequency.

Main Results:

• Attractor self-reproducing is fundamentally linked to periodic initial condition-triggered offset boosting.
• A universal law is established: original position dictates initial phase, attractor size sets amplitude, and reproducing interval determines frequency.
• The product of amplitude and frequency is a constant for a given periodic function.
• Phase space waste occurs with negative slope switching in sinusoidal functions, unless conditional symmetry is re-established.

Conclusions:

• Three-element-oriented offset boosting enhances the designability, achievability, and adjustability of attractor self-reproducing.
• This approach offers significant convenience for various engineering applications.