Computing resilience measures in dynamical systems

Area of Science:

• Dynamical Systems Theory
• Numerical Methods
• Computational Science

Background:

• System resilience, the capacity to withstand disturbances, is increasingly important across disciplines.
• Current resilience metrics often suffer from poor computational accessibility and limited generalizability.
• Dynamical systems theory provides a theoretical foundation for understanding system behavior and stability.

Purpose of the Study:

• To review and reformulate existing resilience measures within a dynamical systems framework.
• To introduce a computationally efficient algorithm for parallel numerical estimation of resilience.
• To develop a generalizable framework for evaluating resilience across changing system parameters.

Main Methods:

• Literature review focused on resilience measures through the lens of dynamical systems theory.
• Reformulation of pertinent resilience measures into a general mathematical form.
• Development of a resource-efficient algorithm for parallel numerical estimation.
• Coupling resilience measures with global continuation of attractors for parameter-dependent evaluation.

Main Results:

• A modular and extensible framework for assessing system resilience was developed.
• The framework allows for consistent evaluation of resilience along system parameter changes.
• Demonstrations on various dynamical systems revealed distinct resilience change patterns.
• The approach provides a more global perspective than traditional local stability metrics.

Conclusions:

• The developed framework offers a comprehensive and accessible method for quantifying system resilience.
• This work facilitates novel research into early warning signals for critical transitions and universal scaling behaviors.
• The open-source computational tools enable system-specific investigations and comparative resilience studies.