Area of research
Statistical and Nonlinear Physics · Cognitive Neuroscience
Research interest
Research topics from publications: The relationship between two fast/slow analysis techniques for bursting oscillations; Mathematical Analysis of Complex Cellular Activity; Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells. Representative work: Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical