The Marketing Book 5th Edition

(a)

0.25

0.20

0.15

0.10

0.05

0.00

r=1.0

(b)

0.63

0.56

r=2.5

0.62

0.61

0.60

0.59

0.58

0.57

0.80 (c)

0.00

r=3.1

0.70

0.60

0.50

0.40

0.30

0.20

0.10

1.00 (d)

0.00

r=3.7001

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

Note: Graphs represent output of the logistic equation: = (1 ), where = 0.5xrt1 t t+0xx x-

240 The Marketing Book

converge exponentially. If = 0, then the
displacements will remain constant over time,
while if > 0, small differences will magnify
over time. All chaotic systems have a lambda
value that is greater than zero.
Initially, the system of interest would have
to be specified in terms of non-linear dynamical
equations. Few researchers in the social scien-
ces have attempted to identify non-linear deter-
ministic behaviours in their systems of interest.
In the main, quantitative research in the social
sciences has tended to be both statistical and
linear in nature. Of course, it is possible that the
appeal of chaos theory may excite an interest in
developing non-linear models.
The researcher would also need to demon-
strate that the system was capable of chaotic
behaviour over some valid region of its para-
meters. By running digital simulations of the
non-linear systems, researchers would hope to
discover regions of chaos in the models that

could be linked with phenomena in the

observed world. Ideally, the Lyapunov expo-

nent could then by calculated and found to be

greater than zero.

Conclusion

The marketing research literature does not

specify which quantitative method is most

‘popular’. One can only conclude that the

multivariate methods, as well as the stochastic

and hybrid techniques and models, are widely

used. Correspondence analysis is a method

with much potential in marketing, as it displays

all the benefits of multidimensional scaling and

can be used with a variety of data inputs. The

flexibility of both simulation and heuristic

programming models mean that they can be

applied to almost any situation where other

Figure 9.8 Output of logistic equation for varying r