All Publications

  • Dynamics of ramping bursts in a respiratory neuron model JOURNAL OF COMPUTATIONAL NEUROSCIENCE Abdulla, M. U., Phillips, R. S., Rubin, J. E. 2022; 50 (2): 161-180


    Intensive computational and theoretical work has led to the development of multiple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full-blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-BötC neuron bursting, along with some parameter adjustments, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature.

    View details for DOI 10.1007/s10827-021-00800-w

    View details for Web of Science ID 000711315300001

    View details for PubMedID 34704174

  • Second Minimal Orbits, Sharkovski Ordering and Universality in Chaos INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS Abdulla, U. G., Abdulla, R. U., Abdulla, M. U., Iqbal, N. H. 2017; 27 (5)