Scaling Laws and Convergence Dynamics in a Dissipative Kicked Rotator

TL;DR

This paper investigates the convergence dynamics of a two-dimensional dissipative kicked rotator, revealing universal scaling laws and critical exponents associated with bifurcations, enhancing understanding of chaos emergence in nonlinear systems.

Contribution

It introduces a generalized approach to analyze convergence in a dissipative kicked rotator, highlighting universal critical exponents and scaling laws near bifurcation points.

Findings

Critical exponents are consistent across models.

Universal scaling laws govern convergence dynamics.

Period-doubling bifurcation plays a key role.

Abstract

The kicked rotator model is an essential paradigm in nonlinear dynamics, helping us understand the emergence of chaos and bifurcations in dynamical systems. In this study, we analyze a two-dimensional kicked rotator model considering a homogeneous and generalized function approach to describe the convergence dynamics towards a stationary state. By examining the behavior of critical exponents and scaling laws, we demonstrate the universal nature of convergence dynamics. Specifically, we highlight the significance of the period-doubling bifurcation, showing that the critical exponents governing the convergence dynamics are consistent with those seen in other models.