Oregonator with Time Delay

maximum time

30

delay time

0

parameter f

0.5

This Demonstration shows how time delay can change the stability of steady or oscillatory Oregonator model states, causing further oscillations or significantly altering existing ones and hence inducing delay-controlled periodic behavior.

From a chemical viewpoint, time delay could cause a stable equilibrium to become unstable and cause the properties in an Oregonator model to fluctuate. The equations describing the Oregonator model with delay are [1]

ϵ

dx

dτ

=qy-xy+x(1-x)

,

δ

dy

dτ

=-qy-xy+fz

,

dz

dτ

=x-z+kz(t-τ)

,

with

x(0)=y(0)=1

, and

z(t≤τ)=1

,

where

t

is time,

x

is

HBrO

2

,

y

is

-

Br

,

z

is

4+

Ce

, and

τ

is a time delay. The parameters are

k=0.1

,

ϵ=4

-2

10

,

δ=4

-4

10

,

q=8

-4

10

, and

f∈[0.4,0.6]

.