Propagation of periodic and chaotic action potential trains along nerve fibers.

*(English)*Zbl 0890.92007Summary: We report the findings that the action potential trains transmitted along the nerve fibers are encoded not only periodically but also chaotically. First, spontaneous action potentials along a single fiber of injured sciatic nerves in the anesthetized rat were recorded. Then, the data were divided into two groups and analyzed with different methods. Phase space representation, spectral analysis and the calculation of correlation dimension were used for the first group of data sampled with constant frequency. Due to the serious influence of the measurement noise, no reliable conclusion can be drawn from them.

For the second group of data of the interspike intervals (ISI) which seem to convey more rich and important information, nonlinear forecasting method, the surrogate data and the plot of ISI(n+1) vs. ISI(n) were used in the analysis. Good results have been obtained which confirm with those from the \(\beta{}\)-cell model. The largest Lyapunov exponent (LLE) was calculated not only to further support our findings of chaos but also to quantitatively determine the degree of chaos.

For the second group of data of the interspike intervals (ISI) which seem to convey more rich and important information, nonlinear forecasting method, the surrogate data and the plot of ISI(n+1) vs. ISI(n) were used in the analysis. Good results have been obtained which confirm with those from the \(\beta{}\)-cell model. The largest Lyapunov exponent (LLE) was calculated not only to further support our findings of chaos but also to quantitatively determine the degree of chaos.

##### MSC:

92C20 | Neural biology |

37N99 | Applications of dynamical systems |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

##### Keywords:

neural electrophysiology; ISI time series; chaos; nonlinear forecasting; surrogate data; largest Lyapunov exponent
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