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Convergent Cross Mapping (CCM) successfully identifies the leading subsystem in coupled systems with time-varying couplings. This method works even with noise and temporal uncertainties, except when subsystem couplings are nearly equal.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Analysis
  • Coupled Oscillator Systems

Background:

  • Physical systems often exhibit time-varying internal couplings, with governing equations frequently unknown.
  • Identifying the leading subsystem (largest average coupling coefficient) is crucial for understanding these systems.
  • Convergent Cross Mapping (CCM) has previously determined causality in systems with constant couplings.

Purpose of the Study:

  • To apply Convergent Cross Mapping (CCM) to coupled Lorenz systems with time-varying coupling coefficients.
  • To investigate CCM's ability to identify the dominant subsystem under various coupling schemes and noise conditions.
  • To assess CCM's performance when dominant subsystems switch over time.

Main Methods:

  • Utilized a pair of coupled Lorenz systems with time-varying coupling coefficients.
  • Implemented four sets of numerical experiments with different coupling schemes (Periodic-constant, Normal, Mixed Normal/Non-normal).
  • Introduced temporal uncertainties and additive normal noise in experiments to simulate realistic conditions.

Main Results:

  • CCM successfully identified the leading subsystem across diverse coupling schemes, including periodic, normal, and mixed variations.
  • The method remained effective even when temporal uncertainties and additive noise were imposed.
  • CCM failed to clearly distinguish a leading subsystem only when average coupling coefficients were approximately equal.

Conclusions:

  • Convergent Cross Mapping (CCM) is a robust method for detecting directional interactions and identifying leading subsystems in complex systems with time-varying couplings.
  • CCM's efficacy is demonstrated even under noisy and uncertain conditions, highlighting its practical applicability.
  • The study confirms CCM's limitation when distinguishing between subsystems with nearly equivalent average coupling strengths.