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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Dynamics and Chaos Theory

Background:

  • Tipping phenomena, or abrupt shifts in system performance due to parameter drift, are of significant interest.
  • Previous research has not extensively explored tipping in systems with chaotic internal dynamics.

Purpose of the Study:

  • To investigate novel tipping phenomena in deterministic systems with chaotic dynamics under parameter drift.
  • To characterize different tipping mechanisms, including fractality-induced and rate-induced tipping.
  • To propose and evaluate tipping probabilities as a measure for chaotic system dynamics.

Main Methods:

  • Utilized a paradigmatic low-dimensional dissipative system with chaotic internal dynamics.
  • Simulated various parameter drift scenarios with non-negligible rates.
  • Numerically determined tipping probabilities and their dependence on system parameters.

Main Results:

  • Observed novel tipping types, including tipping into chaotic attractors and fractality-induced tipping due to complex basins of attraction.
  • Demonstrated that rate-induced tipping occurs gradually, not abruptly, with increasing drift rates.
  • Showcased tipping from/into multiple coexisting attractors and random tipping from chaotic attractors.

Conclusions:

  • Chaotic systems exhibit complex tipping behaviors not seen in simpler systems.
  • Tipping probabilities offer a robust measure for quantifying tipping in chaotic systems.
  • The study highlights the importance of probabilistic approaches for analyzing time-dependent chaotic systems.