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A competition between heteroclinic cycles

Competition between co-existing heteroclinic cycles that have a common heteroclinic connection is considered. A simple model problem, consisting of a system of ordinary differential equations in R4… Expand

When Shil'nikov Meets Hopf in Excitable Systems

- A. Champneys, V. Kirk, E. Knobloch, Bart E. Oldeman, J. Sneyd
- Mathematics, Computer Science
- SIAM J. Appl. Dyn. Syst.
- 5 October 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 intracellular… Expand

Models of Calcium Signalling

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Noisy heteroclinic networks

- D. Armbruster, E. Stone, V. Kirk
- Mathematics
- 17 January 2003

The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching… Expand

Unfolding a Tangent Equilibrium-to-Periodic Heteroclinic Cycle

- A. Champneys, V. Kirk, E. Knobloch, Bart E. Oldeman, J. Rademacher
- Mathematics, Computer Science
- SIAM J. Appl. Dyn. Syst.
- 23 September 2009

An idle detector and safety apparatus for use in an internal combustion engine includes a magnet which is mounted to the carburetor piston valve and a magnetically actuatable switch positioned… Expand

The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit

- V. Kirk, A. Rucklidge
- Mathematics, Physics
- 1 August 2006

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 of system is known… Expand

Understanding and Distinguishing Three-Time-Scale Oscillations: Case Study in a Coupled Morris-Lecar System

- Pingyu Nan, Y. Wang, V. Kirk, J. Rubin
- Mathematics, Computer Science
- SIAM J. Appl. Dyn. Syst.
- 1 September 2015

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Merging of resonance tongues

- V. Kirk
- Mathematics
- 15 July 1993

Abstract This paper considers the resonance behavior found near a saddle-node/Hopf bifurcation in a flow. The global structure of resonance tongues is examined, and it is shown that, in the absence… Expand

On the dynamical structure of calcium oscillations

- J. Sneyd, J. M. Han, +6 authors D. Yule
- Physics, Medicine
- Proceedings of the National Academy of Sciences
- 1 February 2017

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