A method for detecting 'ghost' bifurcations in dynamical systems: application to neural-field models

In this paper we present a method for tracking changes in curvature of limit cycle solutions that arise due to inflection points. We term these changes ‘ghost’ bifurcations, as they appear to be bifurcations when considering a Poincaré section that is tangent to the solution, but in actual fact the deformation of the solution occurs smoothly as a parameter is varied. These type of solutions arise commonly in EEG models of absence seizures and correspond to the formation of spikes in these models. Tracking these transitions in parameter space allows regions to be defined corresponding to different types of spike and wave dynamics, that may be of use in clinical neuroscience as a means to classify different subtypes of the more general syndrome.