An integrative quantifier of multistability in complex systems based on ecological resilience

Area of Science:

• Complex Systems Dynamics
• Ecological Resilience Theory
• Climate Tipping Elements

Background:

• Multistable dynamical systems possess multiple stable states, necessitating robust methods to assess their stability.
• Existing stability concepts (local and global) often address different aspects, leading to an incomplete understanding of system behavior.
• Ecological resilience provides a framework for understanding system persistence and recovery.

Purpose of the Study:

• To propose a novel, pragmatic measure of stability for multistable dynamical systems.
• To integrate various stability aspects into a single, comprehensive metric.
• To develop an early-warning signal for approaching tipping points.

Main Methods:

• Development of the 'integral stability' metric.
• Application and validation of integral stability using exemplary systems: damped driven pendulum, Amazonian rainforest model, and Daisyworld model.
• Comparison with existing local and global stability concepts.

Main Results:

• Integral stability effectively quantifies the stability of different states in multistable systems.
• The proposed measure successfully captures the gradual loss of stability preceding a tipping point.
• Demonstrated applicability across diverse systems, including climate models.

Conclusions:

• Integral stability offers a unified and pragmatic approach to quantifying system stability.
• This new metric serves as a potential early-warning signal for critical transitions.
• Integral stability enhances our ability to predict and manage complex system dynamics.