Quantifying strange property of attractors in quasiperiodically forced systems

Gaolei Li; Denghui Li; Chen Wang; Yuan Yue; Guilin Wen; Celso Grebogi

doi:10.1016/j.physa.2023.129417

Quantifying strange property of attractors in quasiperiodically forced systems

Gaolei Li, Denghui Li^* (Corresponding Author), Chen Wang, Yuan Yue, Guilin Wen, Celso Grebogi

^*Corresponding author for this work

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Abstract

Quasiperiodically forced systems are an important class of dynamical systems exhibiting quasiperiodic, strange nonchaotic, and chaotic attractors. A major concern is the identification of the parameter range in which each one of the attractors is present. In this work, based on the phase sensitivity proposed by Pikovsky and Feudel, we define a measure to quantitatively distinguish quasiperiodic attractors, strange nonchaotic attractors, and chaotic attractors. Particularly, we can determine the boundary points of these three attractors in parameter space. The reliability of this measure is verified in smooth and non-smooth systems.

Original language	English
Article number	129417
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	633
Early online date	11 Dec 2023
DOIs	https://doi.org/10.1016/j.physa.2023.129417
Publication status	Published - 1 Jan 2024

Bibliographical note

This work is supported by the National Natural Science Foundation of China (Nos. 11832009, 12002300, 12072291 and 12362002), and the Natural Science Foundation of Hebei Province, China (Grant No. A2021203013).

Data Availability Statement

No data was used for the research described in the article.

Keywords

Quasiperiodically forced system
Strange nonchaotic attractors
Phase sensitivity

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abstract = "Quasiperiodically forced systems are an important class of dynamical systems exhibiting quasiperiodic, strange nonchaotic, and chaotic attractors. A major concern is the identification of the parameter range in which each one of the attractors is present. In this work, based on the phase sensitivity proposed by Pikovsky and Feudel, we define a measure to quantitatively distinguish quasiperiodic attractors, strange nonchaotic attractors, and chaotic attractors. Particularly, we can determine the boundary points of these three attractors in parameter space. The reliability of this measure is verified in smooth and non-smooth systems.",

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author = "Gaolei Li and Denghui Li and Chen Wang and Yuan Yue and Guilin Wen and Celso Grebogi",

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AU - Li, Gaolei

AU - Li, Denghui

AU - Wang, Chen

AU - Yue, Yuan

AU - Wen, Guilin

AU - Grebogi, Celso

N1 - This work is supported by the National Natural Science Foundation of China (Nos. 11832009, 12002300, 12072291 and 12362002), and the Natural Science Foundation of Hebei Province, China (Grant No. A2021203013).

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N2 - Quasiperiodically forced systems are an important class of dynamical systems exhibiting quasiperiodic, strange nonchaotic, and chaotic attractors. A major concern is the identification of the parameter range in which each one of the attractors is present. In this work, based on the phase sensitivity proposed by Pikovsky and Feudel, we define a measure to quantitatively distinguish quasiperiodic attractors, strange nonchaotic attractors, and chaotic attractors. Particularly, we can determine the boundary points of these three attractors in parameter space. The reliability of this measure is verified in smooth and non-smooth systems.

AB - Quasiperiodically forced systems are an important class of dynamical systems exhibiting quasiperiodic, strange nonchaotic, and chaotic attractors. A major concern is the identification of the parameter range in which each one of the attractors is present. In this work, based on the phase sensitivity proposed by Pikovsky and Feudel, we define a measure to quantitatively distinguish quasiperiodic attractors, strange nonchaotic attractors, and chaotic attractors. Particularly, we can determine the boundary points of these three attractors in parameter space. The reliability of this measure is verified in smooth and non-smooth systems.

KW - Quasiperiodically forced system

KW - Strange nonchaotic attractors

KW - Phase sensitivity

U2 - 10.1016/j.physa.2023.129417

DO - 10.1016/j.physa.2023.129417

M3 - Article

SN - 0378-4371

VL - 633

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 129417

ER -

Quantifying strange property of attractors in quasiperiodically forced systems

Abstract

Bibliographical note

Data Availability Statement

Keywords

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