5 papers · 1 filter
Visibility of heteroclinic networks
Sofia B. S. D. Castro, Claire M. Postlethwaite, Alastair M. Rucklidge
The concept of stability has a long history in the field of dynamical systems: stable invariant objects are the ones that would be expected to be observed in experiments and numeri…
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…
Robust heteroclinic cycles in pluridimensions
Sofia B. S. D. Castro, Alastair M. Rucklidge
Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that does not sat…
Finite switching near heteroclinic networks
S. B. S. D. Castro, L. Garrido-da-Silva
We address the level of complexity that can be observed in the dynamics near a robust heteroclinic network. We show that infinite switching, which is a path towards chaos, does not…
Stability of quasi-simple heteroclinic cycles
Liliana Garrido-da-Silva, Sofia B. S. D. Castro
The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local sta…