Degenerate isostable reduction for fixed-point and limit-cycle attractors with defective linearizations
1Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA.
Physical Review. E
|March 19, 2021
Summary
This study introduces degenerate isostable coordinates for analyzing dynamical systems with defective eigenvalues. This new framework enables reduced-order modeling for systems previously untreatable by standard methods.
Area of Science:
- Dynamical Systems and Control Theory
- Mathematical Physics
- Computational Science
Background:
- Isostable coordinates simplify transient behavior analysis in dynamical systems.
- Current methods focus on nondegenerate isostable coordinates, limiting applications.
- Defective eigenvalues pose challenges for existing isostable reduction techniques.
Purpose of the Study:
- To propose and investigate a degenerate isostable framework for dynamical systems with defective eigenvalues.
- To extend reduced-order modeling capabilities to a broader class of systems.
- To demonstrate the utility of degenerate isostable coordinates in relevant applications.
Main Methods:
- Development of a novel degenerate isostable coordinate framework.
- Application of the framework to reduced-order modeling strategies.
- Investigation of systems exhibiting defective eigenvalues.
Main Results:
- Successful formulation of degenerate isostable coordinates for defective eigenvalues.
- Demonstration that degenerate isostable models retain key properties of nondegenerate models.
- Validation of the framework in circadian physiology and nonlinear fluid dynamics.
Conclusions:
- Degenerate isostable coordinates provide a powerful extension to existing methods.
- This framework broadens the applicability of isostable-based reduced-order modeling.
- The approach is relevant for complex systems in biology and physics.
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