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- ItemGlobal existence of solutions to Keller--Segel chemotaxis system with heterogeneous logistic source and nonlinear secretion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Arumgam, Gurusamy; Dond, Asha K.; Erhardt, André H.We study the following Keller-Segel chemotaxis system with logistic source and nonlinear secretion. For this system, we prove the global existence of solutions under suitable assumptions.
- ItemAnalysis and simulation of a modified cardiac cell model gives accurate predictions of the dynamics of the original one(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Erhardt, André H.; Solem, SusanneThe 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model - like early afterdepolarisations (EADs), which can be precursors to cardiac death - predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to wave break-up leading to cardiac death at the tissue level.