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Title: A mathematical study of complex oscillatory behaviour in an excitable cell model
Author: Baldemir, Harun
ISNI:       0000 0004 7427 3319
Awarding Body: University of Exeter
Current Institution: University of Exeter
Date of Award: 2018
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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.
Supervisor: Tsaneva-Atanasova, Krasimira ; Ashwin, Peter Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: complex oscillations ; bifurcation analysis ; slow-fast analysis