WOLFRAM|DEMONSTRATIONS PROJECT

Gray-Scott Reaction-Diffusion Cell with an Applied Electric Field

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phase-plane diagram at x = 0
time series for a and b at x = 0
δ
0.05
b
0
0.09
electric field
1.
β
130
Consider the Gray–Scott reaction-diffusion cell with an applied electric field. The governing equations and boundary and initial conditions are:
a
t
=
a
xx
-E
a
x
-βa
2
b
,
b
t
=
b
xx
-E
b
x
+βa
2
b
-βδb
,
a
x
=
b
x
=0
at
x=0
,
a=1
and
b=
b
0
at
x=1
and
t=0
.
The time series,
a(t)
and
b(t)
at
x=0
are plotted in orange and blue, respectively. You can vary the values of parameters
b
0
,
β
,
δ
, and
E
. The phase plane diagram is also plotted in magenta.
Various dynamic behaviors are observed: these include (1) a limit cycle and sustained oscillations of
a
and
b
versus time for
(
b
0
,β,δ,E)=(0.09,130,0.05,1)
and (2) a stable node and damped oscillations of
a
and
b
versus time for
(
b
0
,β,δ,E)=(0.09,130,0.06,-0.8)
.