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Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Theoretical physics

Background:

  • Dynamical systems exhibit critical slowing down near bifurcations.
  • Nonautonomous systems present unique challenges in predicting bifurcations.
  • Transcritical bifurcations are fundamental in understanding system state changes.

Purpose of the Study:

  • Investigate critical slowing down in a 2D low-dissipation nonautonomous system.
  • Determine if critical slowing down occurs above the bifurcation point.
  • Analyze the effectiveness of experimental perturbation tests for predicting bifurcations.

Main Methods:

  • Theoretical analysis of a two-dimensional nonautonomous dynamical system.
  • Linear sweeping of a control parameter across a transcritical bifurcation.
  • Experimental perturbation of the system's control parameter.

Main Results:

  • Critical slowing down was observed at parameter values significantly above the transcritical bifurcation point.
  • Experimental perturbations of the control parameter did not alter system behavior.
  • Experimental tests failed to provide information on impending bifurcations.

Conclusions:

  • Critical slowing down can manifest unpredictably in nonautonomous systems.
  • Perturbing the control parameter is an unreliable method for detecting critical slowing down.
  • Theoretical analysis is crucial for understanding the limitations of experimental bifurcation prediction.