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Exploring the adaptive voter model dynamics with a mathematical triple jump
Holly Silk, Güven Demirel, Martin Homer +1
Progress in theoretical physics is often made by the investigation of toy models, the model organisms of physics, which provide benchmarks for new methodologies. For complex system…
Signature stability analysis for networks of coupled dynamical systems with Hermitian Jacobian
Anne-Ly Do, Stefano Boccaletti, Jeremias Epperlein +2
The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what…
Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian
Jeremias Epperlein, Anne-Ly Do, Thilo Gross +1
A linear system , , , with , has a one-dimensional center manifold $E^c = \{v \in \mathbb{R}^n…
Nonlocal Generalized Models of Predator-Prey Systems
Christian Kuehn, Thilo Gross
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability an…
Dynamical analysis of evolution equations in generalized models
Christian Kuehn, Stefan Siegmund, Thilo Gross
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facil…