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…