Negative phase and extended spike-time response curve
© Oh and Matveev; licensee BioMed Central Ltd. 2009
Published: 13 July 2009
The phase response curve (PRC) approach is a powerful tool in analyzing response of spiking cell to synaptic or other perturbations. The PRC-based analysis of the cell response involves describing the effect of perturbation as a change of the phase variable characterizing the state of the spiking cell, whereby the phase is always bounded on the interval [0, 1] or [0, 2π]. However, the extension of phase domain to negative values naturally arises when deriving phase return maps in the case of non-weak inhibition or larger networks coupled by three or more cells, as previously shown by Canavier and coworkers [1, 2].
In our previous work , we have shown that for some biophysical models of spiking cells, a one-dimensional phase reduction of a non-weakly perturbed limit cycle oscillator may require the extension of the phase variable defining the state of the oscillator to a multi-branched phase domain. Such multi-branched domain is most easily implemented by extending the [0, 1] phase interval to negative values. The simplest illustration of such negative phase is provided by the integrate-and-fire model when it is hyperpolarized below its reset potential. This notion of negative phase enables us to extend the phase return map analysis based on the spike-time response curve (STRC) characteristic to describe novel dynamical states of non-weakly coupled oscillators, in particular the alternating-order spiking state.
This work is partially supported by the National Science Foundation grant DMS-0417416.
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