# 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