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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 R4Expand
When Shil'nikov Meets Hopf in Excitable Systems
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 intracellularExpand
Models of Calcium Signalling
This book presents the general modelling theory as well as a large number of specific case examples to show how mathematical modelling can interact with experimental approaches, in an interdisciplinary and multifaceted approach to the study of an important physiological control mechanism. Expand
Noisy heteroclinic networks
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 switchingExpand
Unfolding a Tangent Equilibrium-to-Periodic Heteroclinic Cycle
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 positionedExpand
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
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 knownExpand
Understanding and Distinguishing Three-Time-Scale Oscillations: Case Study in a Coupled Morris-Lecar System
This work is motivated by applications in neural dynamics to focus on a model consisting of a pair of Morris--Lecar systems coupled so that there are three time scales in the full system, explaining the dynamic mechanisms underlying solution features in the three-time-scale model. Expand
Merging of resonance tongues
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 absenceExpand
On the dynamical structure of calcium oscillations
It is shown that Class I Ca2+ oscillations have a common dynamical structure, irrespective of the oscillation period, which allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Expand