21 citations · 94 across the 13 of their papers we have counts for
15 papers
Design of Hierarchical Excitable Networks
Sören von der Gracht, Alexander Lohse
We provide a method to systematically construct vector fields for which the dynamics display transitions corresponding to a desired hierarchical connection structure. This structur…
Complete heteroclinic networks derived from graphs consisting of two cycles
Sofia B. S. D. Castro, Alexander Lohse
We address the question how a given connection structure (directed graph) can be realised as a heteroclinic network that is complete in the sense that it contains all unstable mani…
How many points converge to a heteroclinic network in an aperiodic way?
Christian Bick, Alexander Lohse
Homoclinic and heteroclinic connections can form cycles and networks in phase space, which organize global phenomena in dynamical systems. On the one hand, stability notions for (o…
Arbitrarily large heteroclinic networks in fixed low-dimensional state space
Sofia B. S. D. Castro, Alexander Lohse
We consider heteroclinic networks between nodes where the only connections are those linking each node to its two subsequent neighbouring ones. Using a construct…
Stability Indices of Non-Hyperbolic Equilibria in Two-Dimensional Systems of ODEs
Alexander Lohse
We consider families of systems of two-dimensional ordinary differential equations with the origin as a non-hyperbolic equilibrium. For any number we…
Moduli of stability for heteroclinic cycles of periodic solutions
Maria Carvalho, Alexander Lohse, Alexandre Rodrigues
We consider vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The p…
A hybrid heteroclinic cycle
Sofia Castro, Alexander Lohse
Using a vector field in , we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of…
Almost complete and equable heteroclinic networks
Peter Ashwin, Sofia Castro, Alexander Lohse
Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems wi…
Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks
Christian Bick, Alexander Lohse
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations s…
Simple heteroclinic networks in
Olga Podvigina, Alexander Lohse
We classify simple heteroclinic networks for a -equivariant system in with finite , proceeding as follows: we define a graph associated with…
Pseudo-simple heteroclinic cycles in
Pascal Chossat, Alexander Lohse, Olga Podvigina
We study pseudo-simple heteroclinic cycles for a -equivariant system in with finite , and their nearby dynamics. In particular, in a first step towards a fu…
Boundary crisis for degenerate singular cycles
Alexander Lohse, Alexandre Rodrigues
The term boundary crisis refers to the destruction or creation of a chaotic attractor when parameters vary. The locus of a boundary crisis may contain regions of positive Lebesgue…
Switching in heteroclinic networks
Sofia Castro, Alexander Lohse
We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of…
Construction of heteroclinic networks in
Alexander Lohse, Sofia B. S. D. Castro
We study heteroclinic networks in , made of a certain type of simple robust heteroclinic cycle. In simple cycles all the connections are of saddle-sink type in two-di…
Stability in simple heteroclinic networks in
Sofia B. S. D. Castro, Alexander Lohse
We describe all heteroclinic networks in made of simple heteroclinic cycles of types or , with at least one common connecting trajectory. For networks made of…