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Symmetric and Asymmetric Tendencies in Stable Complex Systems
1Interdisciplinary Graduate School, Nanyang Technological University, 50 Nanyang Avenue, Block S2-B3a-01, 639798 Singapore, Republic of Singapore.
Scientific Reports
|August 23, 2016
Summary
Stable complex systems favor asymmetrical mutualistic/competitive and symmetrical trophic relationships. Increasing interdependence diversity, however, destabilizes these systems, a finding applicable to general stabilization algorithms.
Area of Science:
- Complex Systems Dynamics
- Mathematical Ecology
- Network Stability Analysis
Background:
- System stability is often assessed using Jacobian matrix eigenvalues at equilibrium points.
- All eigenvalues must possess negative real parts for a stable equilibrium.
- Understanding relationship structures in complex systems is crucial for predicting stability.
Purpose of the Study:
- To determine how relationship types (mutualistic, competitive, trophic) influence complex system stability.
- To investigate the impact of interdependence diversity on system stability.
- To propose generalizable stabilization algorithms for complex systems.
Main Methods:
- Analysis of Jacobian matrix eigenvalue bounds in dynamical systems.
- Definition and quantification of interdependence diversity.
- Comparison of theoretical predictions with empirical ecological observations.
Main Results:
- Stable systems exhibit asymmetrical mutualistic/competitive and symmetrical trophic relationships.
- Increased interdependence diversity generally destabilizes equilibrium points.
- Trophic relationships show a greater destabilizing effect from interdependence diversity than mutualistic/competitive ones.
Conclusions:
- Relationship asymmetry/symmetry plays a key role in complex system stability.
- Interdependence diversity is a critical factor influencing stability, with varying effects across relationship types.
- Findings suggest broadly applicable stabilization strategies for diverse complex systems.
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