Phaseamplitude descriptions of neural oscillator modelsTools Wedgwood, Kyle C.A. and Lin, Kevin K. and Thul, Ruediger and Coombes, Stephen (2013) Phaseamplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3 (2). ISSN 21908567
Official URL: http://www.mathematicalneuroscience.com/content/3/1/2
AbstractPhase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strongattraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based MorrisLecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phaseamplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phasereduction technique. As an explicit application of this phaseamplitude framework, we consider in some detail the response of a generic planar model where the strongattraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.
Actions (Archive Staff Only)
