2 ANALYSIS OF
ENTREPRENEURIAL SYSTEM
OF COMPLEX ENTERPRISES
2.1 Dynamics Description of Enterprise
Entrepreneurship
(1) Entrepreneurship Status
If the current state of the enterprise is x
0
and the
continuous entrepreneurial state is x
1
, ... x
k
, ... x
n
, then
the set of enterprise states is: I={x
0
, x
1
,... x
k
,... x
n
}, k
∈[0, n]. The enterprise status here includes enterprise
strategic orientation, share of entrepreneurial
resources, organizational management level
(HUINING, ZHANG XIAONING 2009), core
competitiveness and other internal endowments of the
enterprise, as well as external forms such as market
opportunities, profit levels, and enterprise size, X
k
is
a quantitative description of e elements, x
k
={x
1
k
, x
2
k
,
... x
i
k
, ... x
e
k
}, i={1, 2,... e}. According to the general
phenomenon of enterprise evolution, we can get
Equation (1):
𝑥
=
x
∈(x
+δ,+∞), x
⊂A
x
∈(x
−δ,x
+δ), x
⊂B
x
∈[0,x
−δ), x
⊂C
,
k∈[0,n]
A∪B∪C=I (1)
In this way, the entrepreneurial status of
enterprises is divided into three categories: first, the
enterprise has developed more than the previous time,
which is defined as status A
(LV GUIXING 2006);
Second, the enterprise has no significant change
compared with the last moment, which is defined as
state B; Third, there is a recession compared with the
last moment, which is defined as state C. The
dynamic system acting in A state is recorded as ƒ
A
,
similarly, ƒ
B
, ƒ
C
, but ƒ
A
, ƒ
B
, ƒ
C
are not fixed and can
be transformed into each other.
(2) Environmental Status and Evolutionary Goals
Because the enterprise is not an isolated system, its
entrepreneurial evolution is not only dominated by
the dynamic system formed by its own endowment,
but also affected by the environment. The external
environmental factors that play a key role in
enterprise entrepreneurship mainly include
government mechanism, social mechanism and
market mechanism. Averitt believes that there are two
enterprise clusters in the modern economy, namely,
the core enterprises and the peripheral enterprises
(ZHU Q H, Dou Y J 2007).Hollander pointed out:
"The continuous interaction of market and
technological changes has created opportunities for
the development of enterprises to make up the gap
between mass production and mass circulation,
despite the concentration of resources and economic
forces to huge enterprises…… Enterprises can give
full play to the professional technology and
management capabilities formed by 'product
differentiation' to find the 'gap' in the market"(LI
GENGYIN, HUANG NINGHUI 2001) Translate
these qualitative descriptions into mathematical
language to define the set M of the whole market:
M=M
1
∪G
(2)
(2) M
1
is the collection of a large number of
markets occupied by core enterprises, and G is the
collection of gaps between M1. For M1, it can be
expressed as:
M
1
={m
1
∪m
2
…∪m
i
…∪m
n
},i={1,2, …,n} (3)
(3)
M1 conforms to the mathematical
definition of countable set. When n is finite, M1
is "finite countable set"; When n →+∞, M1 is
"infinitely countable set". Further decompose
the set G:
G=G
1
∪G
2
(4)
(4) G
1
is the gap between the markets occupied by
core enterprises, and G
2
is the gap within the market
occupied by a core enterprise. The combination of G
1
and G
2
includes the gap market of these large core
enterprises. For the whole market set M, it represents
a continuous real number interval, and the
mathematical description is "infinite uncountable
set". Whether M
1
is "finite countable set" or "infinite
countable set", the result of M - M
1
= G is "infinite
uncountable set" (ZUO YALI 2007).
The market of "infinite and uncountable sets" not
only explains the soil and realistic possibility of
enterprise entrepreneurship, but also infers that the
entrepreneurial space of enterprises is huge, which
further indicates that in addition to rapid growth, the
entrepreneurial evolution goal of enterprises is "stable
survival", which is the realistic development status
and development goal that most enterprises should
establish.
(3) Chaos, Criterion and Characteristics of
Entrepreneurship Process
There is chaos in the process of entrepreneurship.
Chaos has the following basic characteristics:
dependence sensitive to initial conditions, internal
randomness, irregular order, etc. These features are
the basis of various chaotic identification methods
(YILANG TAITIAN 1991).
The enterprise conducts entrepreneurial evolution
under the role of the dynamic system. The process can
be described as follows: ƒ: I → I is the mapping of the
entrepreneurial evolution process of the enterprise,
where ƒ is the dynamic system of entrepreneurial