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Chaotic ghosts in systems with parameter drift: Delay and control critical transitions.
Han Su1, Denghui Li2, Jicheng Duan3
1Southwest Jiaotong University, School of Mechanics and Aerospace Engineering, Chengdu 610031, China.
Physical Review. E
|May 16, 2026
Summary
Chaotic ghosts in drifting dynamical systems can delay critical transitions. The delay follows a power-law scaling with the drifting rate, and can be avoided by exceeding a critical parameter reversal rate.
Area of Science:
- Dynamical Systems and Chaos Theory
- Nonlinear Dynamics
Background:
- Parameter drift in dynamical systems can lead to ghost states after bifurcations, influencing transient dynamics.
- The impact of chaotic ghosts on critical transitions in drifting systems remains less explored.
Purpose of the Study:
- Investigate the influence of chaotic ghosts and drifting rates on critical transitions.
- Elucidate the mechanism of delayed transitions caused by chaos.
Main Methods:
- Ensemble perspective analysis of drifting systems.
- Quantification of delayed transition phenomena.
- Power-law scaling analysis with respect to drifting rate.
Main Results:
- Chaotic ghosts significantly influence delayed transitions in drifting systems.
- A mechanism for delayed transition related to chaos was revealed.
- Delayed transition exhibits power-law scaling with the drifting rate.
Conclusions:
- Chaotic ghosts play a crucial role in delayed transitions in drifting systems.
- Parameter reversal rate can prevent critical transitions even after crossing bifurcation points.
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