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- I V Biktasheva, R D Simitev, R Suckley, V N Biktashev
- Philosophical transactions. Series A…
- 2006

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some… (More)

- Rebecca Suckley, Vadim N. Biktashev
- I. J. Bifurcation and Chaos
- 2003

- Rebecca Suckley, Vadim N Biktashev
- Physical review. E, Statistical, nonlinear, and…
- 2003

We analyze the asymptotic structure of two classical models of mathematical biology, the models of electrical action by Hodgkin-Huxley (1952) for a giant squid axon and by Noble (1962) for mammalian Purkinje fibres. We use the procedure of parametric embedding to formally introduce small parameters in these experiment-based models. Although one of the… (More)

- V N Biktashev, R Suckley, Y E Elkin, R D Simitev
- Bulletin of mathematical biology
- 2008

We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the… (More)

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