Coupled catastrophes in systems with bidirectional feedback

Area of Science:

• Complex systems science
• Mathematical modeling
• Dynamical systems theory

Background:

• Catastrophic events are prevalent across diverse scientific disciplines, including ecology and finance.
• Understanding the influence of system interactions on these catastrophes is crucial for prediction and mitigation.

Purpose of the Study:

• To investigate how interactions between two bidirectionally coupled subsystems, each with saddle-node bifurcations, can lead to simultaneous catastrophes.
• To classify the different types of coupled catastrophes and identify the factors influencing their emergence.

Main Methods:

• Analysis of two bidirectionally coupled subsystems exhibiting S-shaped bifurcation curves.
• Development of an analytic/graphical methodology to map coupled catastrophes in parameter space.
• Categorization of coupling classes into cooperation, competition, and predation.

Main Results:

• Identified four types of coupled catastrophes: synchronization, anti-synchronization, consensus, and anti-consensus.
• Demonstrated that the manifestation of these behaviors depends on intrinsic subsystem dynamics and coupling mechanisms.
• Characterized which coupling classes support different types of coupled catastrophes using the developed methodology.

Conclusions:

• System interactions significantly influence catastrophic events, leading to phenomena like synchronization or consensus.
• The interplay between subsystem dynamics and coupling type dictates the emergent catastrophic behavior.
• The developed methodology provides a framework for analyzing and predicting coupled catastrophes across various domains.