AI Article Synopsis
- The study explores the formation of intricate patterns, or "metamorphic tongues," in a system made up of a rotor and a Duffing oscillator, highlighting their unusual quasiperiodic and chaotic behaviors.
- Researchers use Lyapunov exponents to map out self-similar islands of stability and chaos in the system's two-dimensional parameter space.
- Notably, quasiperiodic shrimp-shaped domains exhibit features akin to periodic systems, including complicated behaviors like torus-doubling and torus-tripling.
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.
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