On Coexistence Patterns
Hierarchies of Intricate Partially Symmetric Solutions to Stuart-Landau Oscillators with Nonlinear Global Coupling
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Beschreibung
This book is about coexistence patterns in ensembles of globally coupled nonlinear oscillators. Coexistence patterns in this respect are states of a dynamical system in which the dynamics in some parts of the system differ significantly from those in other parts, even though there is no underlying structural difference between the different parts. In other words, these asymmetric patterns emerge in a self-organized manner.
As our main model, we use ensembles of various numbers of Stuart-Landau oscillators, all with the same natural frequency and all coupled equally strongly to each other. Employing computer simulations, bifurcation analysis and symmetry considerations, we uncover the mechanism behind a wide range of complex patterns found in these ensembles. Our starting point is the creation of so-called chimeras, which are subsequently treated within a new and broader context of related states.
This book is about coexistence patterns in ensembles of globally coupled nonlinear oscillators. Coexistence patterns in this respect are states of a dynamical system in which the dynamics in some parts of the system differ significantly from those in other parts, even though there is no underlying structural difference between the different parts. In other words, these asymmetric patterns emerge in a self-organized manner.
As our main model, we use ensembles of various numbers of Stuart-Landau oscillators, all with the same natural frequency and all coupled equally strongly to each other. Employing computer simulations, bifurcation analysis and symmetry considerations, we uncover the mechanism behind a wide range of complex patterns found in these ensembles. Our starting point is the creation of so-called chimeras, which are subsequently treated within a new and broader context of related states.
Provides the foundation for coexistence patterns as a general class of dynamics Demonstrates how stable chimera states can emerge under purely global coupling Illuminates a wide range of different symmetries attainable by four oscillators
Autor*in
Sindre W. Haugland
Themen in »On Coexistence Patterns«
Coexistence Patterns Chimera States Stuart-Landau Oscillators Global Coupling equivariant Bifurcations Cluster-Splitting Cascade Hierarchy of Solutions Transition From Low to High Complexity Chaotic Itinerancy Stepwise Symmetry-Breaking Symmetry-Increasing Bifurcations Bifurcation Network Nonlinear Dynamics Self-Organized Patterns Multi-Cluster Solutions