Ai: The oscillators with voltage trajectories
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e023.jpg)
and
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e024.jpg)
and phase difference
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e025.jpg)
determine the membrane potential at the ends of a cable with electrotonic length
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e026.jpg)
. Aii: The interaction function
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e027.jpg)
gives the phase shift of oscillator A as a function of
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e028.jpg)
. This interaction function is shifted along the
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e029.jpg)
-axis by the parameters
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e030.jpg)
and
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e031.jpg)
, which capture the oscillator and cable properties, respectively. Aiii: The stable phase-locked solution is determined by
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e032.jpg)
and
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e033.jpg)
and is either at
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e034.jpg)
(e.g. for the solid curve) or at
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e035.jpg)
(e.g. for the dash-dotted curve). Aiv: The stable phase-locked solution as a function of
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e036.jpg)
. The value of
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e037.jpg)
uniquely determines where the in-phase (black solid line) or the anti-phase solution (red dotted line) is stable, given a fixed value of
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e038.jpg)
. B:
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e039.jpg)
as a function of the electrotonic distance
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e040.jpg)
between the oscillators,
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e041.jpg)
ms and
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e042.jpg)
ms (dotted line in panel D). For illustrative purposes we chose
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e043.jpg)
so that the stable in-phase and anti-phase solutions are given by the white and gray areas, respectively. C:
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e044.jpg)
as a function of the membrane resistance
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e045.jpg)
for cable diameter
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e047.jpg)
m, distance between the oscillators 1000
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e048.jpg)
m, membrane capacitance
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e049.jpg)
F/cm
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e050.jpg)
, intracellular resistivity
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e051.jpg)
k
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e052.jpg)
cm and oscillator period
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e053.jpg)
ms. D:
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e054.jpg)
as a function of the oscillator frequency
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e055.jpg)
. The distance between the oscillators is
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e056.jpg)
(dotted line in B),
![](/pmc/articles/instance/2725317/bin/pcbi.1000493.e057.jpg)
ms.