gives us inspirations in exploring the complex
interactions and evolution rules on innovation
system. The study of interrelationships among
species and between species and their physical-
chemical environments in ecology has defined
community as a group of species occurring in a
particular area, and ecosystem as assembles of
species, communities and the physical and chemical
components forming a more or less stable system.
In the early of 1960’, some researchers already
noticed the similar ecological characteristics in
social and economic organization. This lead to
successful findings in the evolution mechanism of
economic communities by Nelson and Winter in
1982. (
Nelson, R.R., Winter, S.G., 1982). Freeman and
Hannan gave a systematic summary of the theory,
methodology and research experience on
organizational ecology. (
Hannan, M.T., Freeman, J.H.,
1989
). Those theory and methodology were also
applied to technology innovation. An innovation
ecological community can be described as some
entities and their inter-relative institutions which
jointly and individually contribute to the
development and diffusion of new technologies. In
1993, Gerry Martin and John Ziman organized a
mult-discipline team to explore the evolution
features and rules of technology innovation from
philosophy, ecology and behavior science. (
Lucheng
Huang, 2004
). Therefore, ecosystem on technology
innovation has been a new hot point. (Lucheng
Huang, 2003
).
In comparison with other innovation
communities, the innovation community of software
enterprise has its unique characteristics. (
Jianping
Wang, 2003
). In the startup stage, software
enterprises usually infest with universities and hi-
tech parks in order to obtain shared talents, capital,
and infrastructures. When entering in the mature
stage, they appear to be inquilinous with some other
industries from a gregarious situation, to avoid
excessive competition. (
Libing Shen, Weihui Dai, 2006;
Nan Ye, 2006
). The “food” sources and “species”
competition play a leading role in the evolution of
software communities. (
Weihui Dai, Mingqi Chen, Nan
Ye, to be published
).
3 LOTKA-VOLTERRA MODEL
The innovation community of the software
enterprise contains some innovation populations,
supporting populations and their environments.
Through the transforming of capital, information and
material, these elements build up a complex and
open system. (
Weihui Dai, Mingqi Chen, Nan Ye, to be
published). To study the competition and its
mechanism in the evolution of software innovation
communities, we used Lotka-Volterra model in this
paper. This model was presented by Lotka and
Volterra in 1925 (
Lotka A. J., 1925), 1926 (Lotka A.J.,
1926
) and 1931 (Volterra. V., 1931) to describe the
quantitative relationship of rival species that in
natural ecosystem.
Lotka and Volterra firstly applied the growth
Logistic equation to the dynamic process of two
competing populations, as shown in (1) and (2)
(
Volterra. V., 1931), where N
1
and N
2
represent the
population size of two species, r
1
and r
2
represent
their In-increase rate, K
1
and K
2
represent their
maximum size of population restricted by resources,
α and β are the competing coefficients of two
species. Competing coefficient is used to represent
the affect and competence imposed by one species to
another. If two species are not in unsolvable conflict,
both α and β are zeros. If they request the exact same
type of resources, both α and β are ones. If species
one consumes a lot more resources than species two,
α is much larger than β.
'
2
CNN
K
rN
rN
dt
dN
−−=
(1)
1112
11
1
()
dN K N N
rN
dt K
−
=
(2)
The Lotka-Volterra competence equation can be
use to describe the competitions among populations
of software companies that adopt different software
technology standards. Let us assume two
populations of application software development
have different technology innovations or different
software technology standards, for example, .NET
platform from Microsoft and J2EE platform from
Sun, noted by population-.NET and population-
J2EE. The sizes of both populations, i.e.
1
N
and
2
N
, can be modelled as (1) and (2). Their sizes
are affected by the self-crowd existing among the
individuals within the same population as well as
competitions among the individuals across different
populations. There are three outcomes of the
competition: either population survives or both
populations survive. Figure 1 shows the density of
both two populations, with the vertical axis as the
density of population-.NET and the horizontal axis
as the density of population-J2EE
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