23 citations · 61 across the 6 of their papers we have counts for
6 papers
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…
Understanding broad-spike oscillations in a model of intracellular calcium dynamics
Behnaz Rahmani, Samuel Jelbart, Vivien Kirk +1
Oscillations of free intracellular calcium concentration are thought to be important in the control of a wide variety of physiological phenomena, and there is long-standing interes…
Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics
Samuel Jelbart, Nathan Pages, Vivien Kirk +2
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond…
Resonance bifurcations of robust heteroclinic networks
Vivien Kirk, Claire Postlethwaite, Alastair M. Rucklidge
Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which…
A mechanism for switching near a heteroclinic network
Vivien Kirk, Emily Lane, Claire M. Postlethwaite +2
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network…
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
Vivien Kirk, Alastair M. Rucklidge
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type…