Quasiperiodic shrimp-shaped domains in intrinsically coupled oscillators

Silvio L T de Souza; Antonio M Batista; Rene O Medrano-T; Iberê L Caldas

doi:10.1063/5.0234904

Quasiperiodic shrimp-shaped domains in intrinsically coupled oscillators

Chaos. 2024 Dec 1;34(12):123146. doi: 10.1063/5.0234904.

Authors

Silvio L T de Souza^{1

2}, Antonio M Batista^{3

4}, Rene O Medrano-T^{5

6}, Iberê L Caldas²

Affiliations

¹ Federal University of São João del-Rei, Campus Centro-Oeste, 35501-296 Divinópolis, MG, Brazil.
² Institute of Physics, University of São Paulo, 05508-900 São Paulo, SP, Brazil.
³ Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
⁴ Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil.
⁵ Department of Physics, Federal University of São Paulo, UNIFESPF, Campus Diadema, 09913-030 Diadema, SP, Brazil.
⁶ Department of Physics, São Paulo State University, UNESP/IGCE, Campus Rio Claro, 13506-900 Rio Claro, SP, Brazil.

PMID: 39671700
DOI: 10.1063/5.0234904

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.