64 citations · 390 across the 24 of their papers we have counts for
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Continuity of projected maps of heteroclinic networks in
David C Groothuizen Dijkema, Claire M Postlethwaite, Alastair M Rucklidge
Stability of robust heteroclinic cycles and networks is typically studied by constructing return maps and analysing their associated transition matrices. This analysis can be simpl…
Local interaction of two systems with saddle-node bifurcations: mutualistic and mixed cases
Peter Ashwin, Claire Postlethwaite, Jan Sieber
The saddle-node bifurcation is the simplest example of a generic bifurcation in smooth ordinary differential equations, and is associated with the creation or destruction of a pair…
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…
Analysis of dynamics near heteroclinic networks in with a projected map
David C. Groothuizen Dijkema, Vivien Kirk, Claire M. Postlethwaite
Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subs…
Travelling waves and heteroclinic networks in models of spatially-extended cyclic competition
David C Groothuizen Dijkema, Claire M Postlethwaite
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be…
Stability of heteroclinic cycles in rings of coupled oscillators
Claire M. Postlethwaite, Rob Sturman
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant…