Neural Comput - Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators.

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Resumo

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Resumo Limpo

investig electr coupl neuron oscil synchron fail synchron use theori weak coupl oscil stabil synchroni antisynchroni predict analyt verifi use numer bifurc diagram shape phase respons curv prc shape voltag time cours frequenc spike freeli vari map region paramet space hold stabl solut find type type prcs can hold synchron antisynchron solut shape prc voltag determin extent stabil achiev introduc fivepiecewis linear model prc threepiecewis linear model voltag time cours analyz result eigenvalu equat determin stabil phaselock solut singl time paramet defin skew prc anoth singl time paramet defin spike width frequenc approach give comprehens pictur relat prc shape voltag time cours stabil result synchron antisynchron solut

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