t2

1
????? ???? - ????? ?????? ?? ?????? ?????? ??????
??????? ????? ???? (???????) -
"???" ????? gtN2-K
"???" ??????
N2
t2
???? ????
2
????? ???? - ????? ?????? ?? ?????? ?????? ??????
??????? ????? ???? (???????) -
"???" ????? gtK-N
????? ????????
Damped oscillation
Chaos
???? ????????
"???" ??????
rgt1 ???????? ????? ????? ?? 2.7!
rlt1 ????? ????????
rgt2 ???????? ?????
rgtgt2 ???? ?????
t3
N2
t2
???? ????
3
????? ???? - ????? ?????? ?? ?????? ?????? ??????
??????? ????? ???? (???????) -
"???" ????? gtK-N
????? ????????
?????? ???? ????? r
????? ???? ?? ????? ????- ???????? ?????? ????
?????? r ? - t
r?lt?/2 (lt1.6)

Damped oscillation
r?gtgt?/2
Chaos
???? ????????
"???" ??????
???????? ?????? (limit cycle) r?gt?/2 ????
????? Nmax- ???? ???? N/Ke r? ?????? ????
r?2, ??? N/Ke27.4, Nmax7.4 K
rgt1 ???????? ????? ????? ?? 2.7!
rlt1 ????? ????????
rgt2 ???????? ?????
t-?
rgtgt2 ???? ?????
t3
N2
t1
t2
?????? ????? ????
??' ??????? ????? ??????? ?- t1
???? ????
???? ????
????? ???? ??????? ?/?? ??????? ?????? ??????
???????
????? ?????
?
4
????? ???????? ????? ????? ?????
r 1.8
???????? ?????
????? ???? ?????? ????? rgt1 - ???? ????? ?
K-N ???? ????? ? K
r 2.3
???????? ?????
N/K
5
????, r ???? ???
????? ???????? ????? rlt1 ????? ???? rgt1 ?????
???????? ?- K rgt2 ???????? ???? K rgt3 ????
r 5.0
????, ???? ?????? ????
r 3.3
????, ???? ?????? ???
r 3.3
???????? 4-??????
r 2.6
N/K
6
???? ????????? ???? ????? ???????? ??? ?????
??????
???? ?????
??????
???????
????
??????
??????
???
???? ?????
????? - ???? ????? ?????? - ???? ????? -
???????? ???? ????- ???
????? - ???? ????? ?????? ???? ????? -
?????? ???? ???? - ??
7
???? ????????? ???? ????? ???????? ??????
??????
????? - ????? ????? ?????? - ?????? ?????? -
???? ????? - ????????? ???? ???? - ???
????? ????? ????? ?????? - ?????? ?????? -
???? ????? ??????, ????? ???? ???? - ???
????? - ????? ????? ?????? ?????? ?????? -
???? ????? ??????, ????? ???? ???? - ???
8
?????? ????? ??????? ?? ??? ???? ??????, ??????
????? ?????? ????? - ???? ????? ?? ?? 84 ?????
????? ????????? ?? 4.5 ?????? ?????

• ?????? ???-?????? (????????) ????? ?????????
• ????? ???? ?"????", ?????? ? N-K
• ????? ?????? ????????? ????? ???????
• ???? ??? ?????? ???? ?????? ??????
• K ?????? ??? ????? ??? ?? ??? ??????
• ????? ?????? ?? ?? ??????, ?? ????
• ????? ?????? ??????? ????? ??? ???

????????? ?????? - ????? ?????? ????
????? ??????? ?????? ????-???? ??????? ?????-????
?"??????" ?? ?????? ?????
???? ?????? ?-?????
9
????? K ?? Pearl Reed ????"? 197 ????? ??? ??
????? ????? ?????? ?? ???? ? - 20 ?????????
?????? ?????, ???? ??????? ?- 200 ?????
?????? ??????????, ????????, ???? ?????
????-?????? ?????? - ?????? -
???? , ???, ????
??????, ??????
?????? ?? ????? ????? ????-?????? ?????,
????????? (??????, ???????) ??????? ?? ??????, ??
???? ??????? ????
??"? ?????? ?? ?????? ?????? ????? ??/? ??????
????? ????? ?????? ?? ?????? ?????? ??? ?????
???? ?? ????? ?????? ?????, ?? ?? ????? ??????
????? ??? ????? ???????? ?? ????
10

• ????? ?? ??? ?????????? ?????? ??? ????
• ????????
• ?????

???? ???? ???????
N
K
?? ???? "???? ????? ?? ????"?
t
??? ? ?????? ????????? ?????? ????????? ?
?????????
??? ?"???" ???? ???? ????? ????? ????
11
????????? (????) r ?????????? (????) K ?????
????? ?????? r ?? ?????? K ??? ???????
???? ??????? ????
?????
??? a
??? b
4
2
?? ????
22
42

• ?????

• ?????

?? ????? ??????
????? ???? ??????
????? ????? ???? ?????? ??? ???? ??????
?????, b ????? ???? ?? ??? ???????
??? 1 1 ??? 2 2 ??? 3 4
??? 1 1 ??? 2 4 ??? 3 16
?????? ???? ????? ??????
???? 4 ?? 20 ??? ??? ????? ??? ? 10 ???? ??????
???? 10?????, 50
???? 2 ?????? 2 ??? 4 4
???? 8 ?????? 8 ??? 4 64
???? ??? ?? ????????? ??? ?????? ??????
?????? ?????? ???? ?????? ???? ????? ??? ???
?????? ????? ?????? ???? ?????? ????
????? ????? ?????? ??? ?????? ?????? ??
?????????, ?????