Different classifications of UPOs in the parametrically different chaotic ISI series of a neural pacemaker

Abstract

Various interspike intervals (ISIs) in a series of spontaneous discharges of experimental neural pacemakers were identified as chaotic and as lying between stable period 2 and stable period 3. The method of So et al. for detection of unstable periodic orbits (UPOs) was applied to analyze two chaotic ISI series generated under the action of [Ca2+]o in different concentrations. In the chaotic ISI series near the stable period 2, an unstable period 2 orbit was detected. In the chaotic ISI series near the stable period 3, both an unstable period 2 orbit and an unstable period 3 orbit were detected. The location of the unstable period 2 orbit was close to that of the stable period 2 in the return map, while the location of the unstable period 3 orbit was close to that of the stable period 3. The results not only revealed the structures of various chaotic ISI series, but also indicated that the classification of UPOs could reflect the experimental control parameters at which the chaotic ISI series were generated. The previously discovered period adding bifurcation in the ISI series generated by experimental neural pacemakers [12] was further described in terms of the evolution of the period orbits.