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Route to extreme events in a parametrically driven position-dependent nonlinear oscillator.

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Summary

This study reveals two new ways extreme events (EE) emerge in a complex oscillator system. These sudden, large chaotic oscillations are linked to specific changes in system dynamics and bifurcation routes.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • The Mathews-Lakshmanan oscillator is a key model for studying nonlinear phenomena.
  • Understanding the conditions leading to extreme events (EE) is crucial in various scientific fields.
  • Position-dependent mass terms introduce complex dynamics not fully explored in driven oscillators.

Purpose of the Study:

  • To investigate the bifurcation routes leading to extreme events (EE) in a damped and driven Mathews-Lakshmanan oscillator with a position-dependent mass.
  • To characterize the dynamics of quasiperiodic (QP), strange non-chaotic (SNA), and chaotic attractors associated with EE.
  • To identify the mechanisms, specifically interior crisis, responsible for the sudden onset of EE.

Main Methods:

  • Analysis of bifurcation routes using damping parameter variations.
  • Characterization of dynamical states via Lyapunov exponent spectrum.
  • Application of singular spectrum analysis and the 0-1 test for QP and SNA dynamics.
  • Definition and identification of EE based on a pre-defined threshold height.

Main Results:

  • Two distinct bifurcation routes to EE were identified: QP -> SNA -> Chaotic (EE) and QP -> Chaotic (EE).
  • Extreme events emerge due to the sudden expansion of the chaotic attractor via interior crisis.
  • The study provides the first report of EE arising from these specific bifurcation pathways.
  • Lyapunov exponent spectrum, singular spectrum analysis, and 0-1 test were used to distinguish dynamical regimes.

Conclusions:

  • The Mathews-Lakshmanan oscillator with position-dependent mass exhibits complex dynamics leading to extreme events through novel bifurcation routes.
  • Interior crisis is a key mechanism for the sudden appearance of large-amplitude chaotic oscillations (EE).
  • This research advances the understanding of extreme event generation in nonlinear systems.