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- 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)

- 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

- V N Biktashev, R Suckley
- Physical review letters
- 2004

Models of electric excitability of cardiac cells can be studied by singular perturbation techniques. To do this one should take into account parameters appearing in equations in nonstandard ways. The physical reason for this is near-perfect switch behavior of ionic current gates. This leads to a definition of excitability different from the currently… (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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