By Stavros N. Busenberg (auth.), Luigi Salvadori (eds.)

ISBN-10: 3540129316

ISBN-13: 9783540129318

ISBN-10: 3540388125

ISBN-13: 9783540388128

**Read or Download Bifurcation Theory and Applications: Lectures given at the 2nd 1983 Session of the Centro Internationale Matematico Estivo (C.I.M.E.) held at Montecatini, Italy, June 24 – July 2, 1983 PDF**

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**Extra info for Bifurcation Theory and Applications: Lectures given at the 2nd 1983 Session of the Centro Internationale Matematico Estivo (C.I.M.E.) held at Montecatini, Italy, June 24 – July 2, 1983**

**Example text**

T, Here, denotes the number of i n d i v i d u a l s , per unit age and u n i t spatial volume length, i f space is one-dimensional), who are of age position a, x. By ~ i ( a ) and Bi(a) a at time t and at we denote the i n t r i n s i c death rate per u n i t age, and the i n t r i n s i c b i r t h rate per unit age, of i n d i v i d u a l s in the i t h populat i o n who are of age a. The t o t a l i t h population density is given by Pi(t,x) = ui(a,t,x)da. 0 48 Then the basic equations governing the dynamics of the i t h population are au.

1962). Cliffs. F. (1845). "Recherches mathematiques sur la loi d'accroissement de la population", Nouveau Mem. Acad. Sci. Bruxelles, 18: 3-41. [23] Volterra, V. (1939). "The general equations of biological s t r i f e in the case of historical actions", Proc. Edinburgh Math. Soc. 6: 4-I0. [24] Volz, R. (1982). "Global asymptotic s t a b i l i t y of a periodic solution to and epidemic model", J. Math. Biol. 15: 319-338. Matrix Iterative Analysis, Prentice Hall, Englewood 31 CHAPTER I l l BIFURCATION OF PERIODIC SOLUTIONS I.

2) dxi (t) dt = aixi_l(t) - bixi(t), The result of Mahaffy is as follows. i = 2. . . n. 1. (i) Assume that There exists 6 > O, and c with ac > b(eBr-l) -I where n = 11 a j / b j , B : min(b,b 2 . . . tion is satisfied for large enough r ) . (ii) r is large enough that n-I arctan ~ + Z j=2 n (iii) ](b+ir) arctan ~ n Z (bj+iv)l < -( II aj)f'(O) j=2 j=2 constant periodic s o l u t i o n . for a l l < ~ . j r. In p a r t i c u l a r , i f Moreover, f o r any n b( R Then equation. 2) has a periodic solution for all large enough r .

### Bifurcation Theory and Applications: Lectures given at the 2nd 1983 Session of the Centro Internationale Matematico Estivo (C.I.M.E.) held at Montecatini, Italy, June 24 – July 2, 1983 by Stavros N. Busenberg (auth.), Luigi Salvadori (eds.)

by George

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