. . 11, 1(7), 2009 517.958:57 © 2009 . , . , . e-mail: oksana-rev@mail.ru, frisman@mail.ru ; . , . , . : . , , , , - . . ;P- [5-7] n- - ; F, M , . - [2-4]. , - . Pn 1 Fn 1 Mn r Fn (1 1 , , « » [1, 8, 10]. , ) w2 Pn s2 M n (1) r- , - , , s1Fn w1Pn , - s1 , w1 s2 , w2 . , r , r , a - - aM hF M , , (2) , , - ( , ), . . , . , h , h, - - . . h : - , : , , h, , , 1564 . , - s > 0, 1, max w1 1 , 1 P w2 - 1 , , 2P . , . , = -1 - - | 1). a, - , (1) -« » mn 1 ( 1 , (| ) fn | . - (s1 = s2 = s). 1 2 , ( pn | mn af n 1 - : 2(hf m ) 2 . (hf 2 (2 p 1) m 2 (2bp 1) a hf n mn 0,5(1 bpn ) pn sf n 0,5(1 pn ) pn smn , (2) (2) , - m - : ) . b= (3), / f p. p 1 / 2b 1 C bA 1 2 p p (1 p ) , 2(1 s) 2 h (1 s ) . ab C , 1. (2), - , 1 , , ( 2 s) s - 0, G 2 G a - 1 ( 4 4 s a) . 2 ( 4 2sh 4 s 2h a) b 0 b 1, p 1/ b b 1, a 2((1 s ) h(1 v)), 0 p 1 / 2b . p 1 / 2b b : p . . (3) , 0 1/ 2 , 4(C A) , 1 (bA C 1) 2 p (1 bp ) , m 2(1 s ) 2s a 2 , A ab f )p (4) 1 , 8b(1 s ) p 1 / 2b , f m 2b 1 . 8b 2 (1 s ) m/ f 2 hf (2 p 1) m (2bp 1) . 2(hf m ) 2 ( 2b 1) / b , b b > 1/2. (4) , l=s p 1 / 2b , 1. 2 1 1 2 s s , 0. G s, 2 - 1 2 1 a G. max 0, 1565 h 2(1 h )(1 s ) , h( h(3 2 s ) 2 8(1 s)). (5) (5) , , - . . 11, 1(7), 2009 - ( . - ) , . 1). . 1. ( ) 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 a ( 1( . ). h, - . 2 ). a ( - (s) , « » ), s - : 7h 6 8( h 1) h(9h 8) 8( h 1) . 2 ). s 1, . 2. a ) (p) ( (2) ) : ) h = 0,01, ) a = 1,84 (m) 2. ( ) (2) , 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) , , . 3). b < 2. , p 1/ 2 , a > 1. : - . 3. ( ) 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 , , , ( . . - - ) . [9], : , , ) , . ( , , . , , ( ) - , . , . , - [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 a local northern fur seal with seal herd // Ecological Modelling, 1982. V. 16. P. 151-172. 2. Hastings A. Age dependent dispersal is not a simple process: Density dependence, stability, and chaos // Theor. Popul. Biol. 1992. V. 41, 3. P. 388-400. 3. Kooi B.W. and Kooijman S.A.L.M. Discrete Event versus Continuous Approach to Reproduction in 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 // 1567 . . 11, 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. 6. Leslie P.H. On the use of matrices in certain population mathematics. Biometrika. 1945. V. 33, 3. P. 183-212. 7. ., . : // . ., 2007. . 13, 4. . 145-164. 8. ., ., . 1(7), 2009 . . . , . // 9. . 1980. . 41, . 2. . 270-278. // 1994. . 338, 10. 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. 1568