The Morris-Lecar model is a conductance-based dynamical system for electrical oscillations in an excitable membrane (Morris and Lecar
1981). In its planar form, the calcium gate is set to its instantaneous equilibrium
value. The remaining variables are the membrane voltage 
and the fraction 
of open potassium channels. The ordinary
differential equations are
 |  |  |
(1)
|
 |  | ![phicosh((V-V_3)/(2V_4))[w_infty(V)-w],](/images/equations/Morris-LecarModel/Inline8.svg) |
(2)
|
where 
and 
are functions of time and primes denote derivatives
with respect to 
. The constant 
is capacitance, 
is applied current, and 
and 
are the maximal conductance and reversal potential for the
leak, calcium, and potassium terms. The gate functions are
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
and 
are the half-activation voltages, 
and 
are nonzero voltage scales, and 
sets the potassium gate rate. The 
-nullcline is 
. Since 
, the interval ![[0,1]](/images/equations/Morris-LecarModel/Inline30.svg)
is invariant for the gate.
For example, take 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, and 
. Numerical integration
from the initial state 
shows approach to a periodic
orbit. The planar model allows the onset of oscillations to be studied through
intersections of its nullclines and changes in the
stability of the resulting equilibria (Morris
and Lecar 1981).
