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Robust Heteroclinic Cycles in Pluridimensions
Sofia B S D Castro1, Alastair M Rucklidge2
1Centro de Matemática and Faculdade de Economia, Universidade do Porto, Porto, Portugal.
Journal of Nonlinear Science
|June 16, 2025
Summary
This study introduces robust heteroclinic cycles in pluridimensions, extending stability theory beyond traditional eigenvalue conditions. New methods allow analysis even when equilibria lack contracting eigenvalues, with applications in population dynamics.
Area of Science:
- Dynamical Systems Theory
- Mathematical Biology
Background:
- Heteroclinic cycles connect equilibria in dynamical systems.
- Traditional stability analysis relies on eigenvalue properties within flow-invariant subspaces.
Purpose of the Study:
- Investigate robust heteroclinic cycles in pluridimensions.
- Develop a stability theory for cycles lacking contracting eigenvalues.
Main Methods:
- Analysis of heteroclinic cycles not confined to subspaces of equal dimension.
- Development of novel stability criteria for these complex cycles.
Main Results:
- Established stability theory for robust heteroclinic cycles in pluridimensions.
- Demonstrated applicability through four novel 4-dimensional examples.
Conclusions:
- The new theory accommodates cycles where equilibria lack contracting eigenvalues.
- Provides a framework for modeling complex population dynamics with transitions between mixed states.
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