Chlorite-Iodide-Malonic Acid (CIMA) Reaction

a

37.4827

b

11.4654

time series

phase plane

stability diagram

0

5

10

15

20

0

20

40

60

80

100

120

time

u(t), v(t)

The Demonstration presents the chlorite-iodide-malonic acid (CIMA) reaction, which gives rise to temporal oscillations.

The reaction scheme is:

A→X

X→Y

4X+Y→P

,

where

X=I

-

and

Y=ClO

-

2

.

The dimensionless governing equations are:

u

τ

=a-u-4uv/(1+u

2

)

,

v

τ

=b(u-uv/(1+u

2

))

.

Oscillating patterns are observed for

b<

3a

5

-

25

a

. In fact, oscillations are obtained in snapshot 1 for

b=11.4655

and

a=37.4828

. The phase-plane diagram shows a limit cycle.

On the other hand, a stable steady state is found for

a=21.7989

and

b=15.7884

(snapshot 3). Phase-plane analysis shows a stable node. The locations of the selected parameter values are plotted in the stability diagram that demarcates the parameter space between limit cycles (periodic oscillations) and damped oscillations.