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