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- W2031631993 abstract "We study the asymptotic dynamics of a coupled system of ordinary differential equations, which arises from a model of a network of cells coupled by gap junctions. The variables in this model are the electrochemical potentials of a chemical species in each cell and the states of the various gap junctions. The dynamics of the chemical species is much faster than that of the gap junctions leading to a singular perturbation problem. We show that for biologically realistic parameters, the system has a globally attracting smooth invariant manifold which is the graph of a function from gap junction states to electro-chemical potential. It is therefore the gap junction dynamics which controls the overall behaviour of the system. Rather than using a standard singular perturbation approach, which fails to give explicit estimates of the size of allowed perturbations, we employ inertial manifold techniques. These are usually applied to systems of the form where u belongs to Hilbert space and A is a positive linear operator satisfying a so-called 'gap condition'. Since our system fails to meet this condition, we generalize these methods to a class of systems of the form" @default.
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- W2031631993 date "1998-01-01" @default.
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- W2031631993 title "Inertial manifolds for dynamics of cells coupled by gap junction" @default.
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- W2031631993 doi "https://doi.org/10.1080/02681119808806260" @default.
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