Universal scaling laws of chaotic escape in dissipative multistable systems subjected to autoresonant excitations

TL;DR

This paper develops universal scaling laws for chaotic escape in dissipative multistable systems under autoresonant excitations, combining theoretical derivations with numerical validation to understand transient chaos behavior.

Contribution

It introduces a comprehensive theoretical framework for predicting chaotic escape dynamics and scaling laws in dissipative multistable systems influenced by autoresonant excitations.

Findings

Derived universal scaling laws for chaos onset and lifetime

Validated robustness of scaling laws against noise

Demonstrated applicability to reshaped systems

Abstract

A theory concerning the emergence and control of chaotic escape from a potential well by means of autoresonant excitations is presented in the context of generic, dissipative, and multistable systems. Universal scaling laws relating both the onset and lifetime of transient chaos with the parameters of autoresonant excitations are derived theoretically using vibrational mechanics, Melnikov analysis, and energy-based autoresonance theory. Numerical experiments show that these scaling laws are robust against both the presence of noise and re-shaping.