Applicability of 0-1 Test for Strange Nonchaotic Attractors

TL;DR

This paper demonstrates that the 0-1 test can effectively distinguish strange nonchaotic attractors from other attractors and detect transitions between different dynamical states in various systems.

Contribution

It shows how to adapt the 0-1 test for identifying SNAs by choosing parameters based on the golden mean, and applies it to multiple dynamical systems.

Findings

0-1 test successfully distinguishes SNAs from other attractors.

The test detects transitions from quasiperiodic to chaotic motion via SNAs.

Application to logistic map, cubic map, and Duffing oscillator confirms effectiveness.

Abstract

We show that the recently introduced 0-1 test can successfully distinguish between strange nonchaotic attractors(SNAs) and periodic/quasiperiodic/chaotic attractors, by suitably choosing the arbitrary parameter associated with the translation variables in terms of the golden mean number which avoids resonance with the quasiperiodic force. We further characterize the transition from quasiperiodic to chaotic motion via SNAs interms of the 0-1 test. We demonstrate that the test helps to detect different dynamical transitions to SNAs from quasiperiodic attractor or the transitions from SNAs to chaos. We illustrate the performance of the 0-1 test in detecting transitions to SNAs in quasiperiodically forced logistic map, cubic map, and Duffing oscillator.