Gray-Scott Reaction-Diffusion Cell with an Applied Electric Field
Gray-Scott Reaction-Diffusion Cell with an Applied Electric Field
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
a
x
2
b
b
t
b
xx
b
x
2
b
a
x
b
x
x=0
a=1
b=
b
0
x=1
t=0
The time series, and at are plotted in orange and blue, respectively. You can vary the values of parameters , , , and . The phase plane diagram is also plotted in magenta.
a(t)
b(t)
x=0
b
0
β
δ
E
Various dynamic behaviors are observed: these include (1) a limit cycle and sustained oscillations of and versus time for and (2) a stable node and damped oscillations of and versus time for .
a
b
(,β,δ,E)=(0.09,130,0.05,1)
b
0
a
b
(,β,δ,E)=(0.09,130,0.06,-0.8)
b
0