Work

Quasiperiodic shrimp-shaped domains in intrinsically coupled oscillators

Year: 2024

Type: article

Abstract: We report remarkable pattern formation of quasiperiodic domains in the two-dimensional parameter space of an intrinsically coupled system, comprising a rotor and a Duffing oscillator. In our analysis, we characterize the system using Lyapunov exponents, identifying self-similar islands composed of intricate regions of chaotic, quasiperiodic, and periodic behaviors. These islands form structures with an accumulation arrangement, denominated here as metamorphic tongues. Inside the islands, we observe Arnold tongues corresponding to periodic solutions. In addition, we surprisingly identify quasiperiodic shrimp-shaped domains that have been typically observed for periodic solutions. Similar features to the periodic case, such as period-doubling and secondary-near shrimp with three times the period, are observed in quasiperiodic shrimp as torus-doubling and torus-tripling.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0234904

Authors: Silvio L. T. de Souza, Antonio M. Batista, Rene O. Medrano-T, Iberê L. Caldas

Institutions: Federal University of São João del-Rei, Universidade de São Paulo, Universidade Estadual de Ponta Grossa, Universidade Estadual Paulista (Unesp), Universidade Federal de São Paulo

Language: English

Topic: Chaos control and synchronization

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Fundação de Amparo à Pesquisa do Estado de São Paulo

Awards: G1956105210, Characterization of Parameter Space for Nonlinear Systems, G7309294458, Basins of Attraction: From unidimensional maps to complex networks