Return to search

A mathematical study of complex oscillatory behaviour in an excitable cell model

Inner hair cells (IHCs) are the actual sensory receptors in hearing. Immature IHCs generate spontaneous calcium-dependent action potentials. Changing the characteristic of the Ca2Å signals modulates the amplitude and duration of the action potentials in these cells. These spontaneous action potential firing patterns are thought to be important for the development of the auditory system. The aim of this thesis is to gain a deeper understanding of the electrical activity and calcium signalling during development of IHCs from a mathematical point of view. A numerical bifurcation analysis is performed to delineate the relative contributions of the model parameters to the asymptotic behaviour of the model. In particular, we investigate the pattern of periodic solutions including single (normal) spiking, pseudoplateau burstings and complex solutions using two-parameter sections of the parameter space. We also demonstrate that a simplified (three-dimensional) model can generate similar dynamics as the original (four-dimensional) IHC model. This reduced model could be characterised by two fast and one slow or one fast and two slow variables depending on the parameters’ choice. Hence, the mechanisms underlying the bursting dynamics and mixed mode oscillations in the model are studied applying 1-slow/2-fast and 2-slow/1-fast analysis, respectively.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:754277
Date January 2018
CreatorsBaldemir, Harun
ContributorsTsaneva-Atanasova, Krasimira ; Ashwin, Peter
PublisherUniversity of Exeter
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://hdl.handle.net/10871/34029

Page generated in 0.002 seconds