математическая модель динамики численности популяции

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. . 11,
1(7), 2009
517.958:57
© 2009
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e-mail: oksana-rev@mail.ru, frisman@mail.ru
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a
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8b 2 (1 s )
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2
hf (2 p 1) m (2bp 1) .
2(hf m ) 2
( 2b 1) / b
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b
b > 1/2.
(4)
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p 1 / 2b
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1.
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h 2(1 h )(1 s )
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h( h(3 2 s ) 2 8(1 s)). (5)
(5)
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. . 11,
1(7), 2009
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. 1).
. 1.
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p 1/2 b , h = 0,01:
) a = 1,79779, b = 0,521075926, s = 0,6; ) a = 1,845, b = 0,516877637, s = 0,6;
) a = 0,78901, s = 0,8, b = 0,366577718
h < 0,5
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s 1,
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a
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(p)
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(2)
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(m)
2.
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(2)
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p
1/ 2.
p 1/ 2,
b
,
s = 0,6.
.
1566
,
-
b
2
2 4 sh 2s 4h a .
4h 4 sh a
a 1 2(1 2h)(1 s)
(3 2s) 2 8h(1 s) . (6)
(6)
-
.
p 1/ 2, f
1 .
2 b ,
m
8(1 s )
8(1 s)
m / f 1 /(2 b)
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b < 2.
,
p 1/ 2
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a > 1.
:
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. 3.
(
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p 1/2 b , h = 0,01:
) a = 2,3999, s = 0,9, b = 1,159628556; ) a = 2,409, s = 0,9; b = 1,162829636,
) a = 5,15, s = 0,5, b = 1,610136452
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[1, 8].
(
09-I- 15-01, 09-I-12, 09-II06-006),
(
09-04-00146),
(
08-01-98505).
-
1. Frisman E.Ya., Skaletskaya E.I. Kuzyn A.E. A
mathematical model of the population dynamics of
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process: Density dependence, stability, and chaos
// Theor. Popul. Biol. 1992. V. 41, 3. P. 388-400.
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Structured Population Dynamics // Theor. Popul.
Biol. 1999. V. 56. 1. P. 91-105.
4. Lebreton J.D. Demographic Models for Subdivided
Populations: The Renewal Equation Approach //
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Theor. Popul. Biol. 1996. V. 49, 3. P. 291-313.
5. Lefkovitch L.P. The study of population growth in
organisms grouped by stages // Biometrics. 1965.
V. 21, P. 1-18.
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3. P. 183-212.
7.
.,
.
:
//
. ., 2007. . 13,
4. .
145-164.
8.
.,
.,
.
1(7), 2009
.
.
.
,
.
//
9.
. 1980. . 41,
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2. . 270-278.
//
1994. . 338,
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2. . 282-286.
.,
.,
.
-
Cervus nippon
//
.
. 1988.
2.
COMPLEX DYNAMIC MODES OF POPULATION
WITH AGE AND SEX STRUCTURE
© 2009 O.L. Revutskaya, E.Ya. Frisman
Institute for Complex Analysis of Regional Problems Far-Eastern Branch Russian Academy of Science,
Birobidzhan; e-mail: oksana-rev@mail.ru, frisman@mail.ru
We consider the nonlinear three-componential model of population number dynamics. It considers the sex and age
structure dynamics and density-dependent effects impact on survival rates of a younger age class. We consider two
special cases of the model, when maximum equilibrium number of females or males exists. We investigate some scenarios
of the stabilized number transition to nonlinear modes of dynamics.
Key words: population models, age and sex structure, stability, dynamic modes, chaos.
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