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Abstract
An approximate analytical solution
characterizing initial conditions leading to action potential firing
in smooth nerve fibres is determined, using the bistable equation.
In the first place, we present a non-trivial stationary solution
wave. Then, we extract the main features of this solution to obtain
a frontier condition between the initiation of the travelling waves
and a decay to the resting state. This frontier corresponds to a
separatrix in the projected dynamics diagram depending on the width
and the amplitude of the stationary wave.
Mathematics Subject Classification: Primary: 92C20, 35K57; Secondary: 58E30.
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