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- Alan R. Champneys, Vivien Kirk, Edgar Knobloch, Bart E. Oldeman, James Sneyd
- SIAM J. Applied Dynamical Systems
- 2007

This paper considers a hierarchy of mathematical models of excitable media in one spatial dimension, specifically the FitzHugh-Nagumo equation and several models of the dynamics of intracellularâ€¦ (More)

- Alan R. Champneys, Vivien Kirk, Edgar Knobloch, Bart E. Oldeman, Jens D. M. Rademacher
- SIAM J. Applied Dynamical Systems
- 2009

The dynamics occurring near a heteroclinic cycle between a hyperbolic equilibrium and a hyperbolic periodic orbit is analyzed. The case of interest is when the equilibrium has a one-dimensionalâ€¦ (More)

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al., "A method forâ€¦ (More)

- Je-Chiang Tsai, Wenjun Zhang, Vivien Kirk, James Sneyd
- SIAM J. Applied Dynamical Systems
- 2012

- Sebastian Boie, Vivien Kirk, James Sneyd, Martin Wechselberger
- Journal of theoretical biology
- 2016

Many biophysical models have the property that some variables in the model evolve much faster than others. A common step in the analysis of such systems is to simplify the model by assuming that theâ€¦ (More)

- Saeed Farjami, Vivien Kirk, Hinke M. Osinga
- SIAM J. Applied Dynamical Systems
- 2018

- Vivien Kirk, Edgar Knobloch
- I. J. Bifurcation and Chaos
- 2004

We consider a bifurcation that occurs in some two-dimensional vector fields, namely a codimension-one bifurcation in which there is simultaneously the creation of a pair of equilibria via a steadyâ€¦ (More)

- James Sneyd, Jung Min Han, +6 authors David I. Yule
- Proceedings of the National Academy of Sciencesâ€¦
- 2017

Oscillations in the concentration of free cytosolic Ca2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms thatâ€¦ (More)

- Jung-Min Han, Akihiko Tanimura, Vivien Kirk, James Sneyd
- PLoS Computational Biology
- 2017

Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestionâ€¦ (More)

- Vivien Kirk, Claire M. Postlethwaite, Alastair M. Rucklidge
- SIAM J. Applied Dynamical Systems
- 2012

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 typically result inâ€¦ (More)