533 citations · 1.6k across the 54 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…
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…
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…
Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock
Claire M Postlethwaite, Alastair M Rucklidge
The well-known game of Rock--Paper--Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the…
Localized patterns in periodically forced systems
A S Alnahdi, J Niesen, A M Rucklidge +1
Spatially localized, time-periodic structures are common in pattern-forming systems, appearing in fluid mechanics, chemical reactions, and granular media. We examine the existence…
Skew-Varicose Instability in Two Dimensional Generalized Swift-Hohenberg Equations
J. A. Weliwita, A. M. Rucklidge, S. M. Tobias
We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupl…