Tipping phenomena in typical dynamical systems subjected to parameter drift.

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.