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e E E E E Peee copeex ooecx poe ee e oo aoe ayoe, o oee aee eoeeca. Ocoy po ec popeae yee a ooecx poecco, apaeoe a papaoy eoo poopoa pa ooecx cce x oaoo ypae epecax eoea.

O ax ye o apae ec aeaecoe oepoae poecco epo- accooea oeoeoe, oope oeac oacc ee ooecx cce.

M paccop ocoe oe a ceoc oy occeax, y a opao a x ocoe oo xapaepoa ycooc ooecx cooec poopoa x oeee o pee.

Paccop oeee oeo o oy, e ya o e ee aoec c py a, axoc c e o a oo, o a pyx poecx ypox. pocee ypae, ocae eopae poc oy ycox a eca (apep, eox po yaope), ye paccope e 1 (1.1)(1.3).

Hao, o ypaee (1.3) oceco po epxca oyaec p yee caoopae poca ("caoopae") oy ycox eco oype yp oy. Oo ee M x 0 x / x (5.1), Mt e e /x, poopoa oecy cpe ey oco yp oy, yae o e caoopae poca.

eo e, o ypaee caoapx coco 0 x / x0 ee a op:

x, 0 0 x.

/ 52 Coaco pep ycooc (1.17) a pooo pao ac (5.1) f (x ) = - 2 x (5.2) caoapo oe opeee ee ycooc. oca aee x1 =, epoo caoapoo pea oy, o f = 0 x1=0(x) 0 .e. cocoe, e x1 =, eycoo.

0 Haoopo, pyoe caoapoe cocoe x2 = ycoo, a a cea f =-.

x2 (x) cooe cocoe x2 = = xmax cooecye aca/ o caoapo ceoc oy, "eoc cpe", ooo ax ycox. a o, ea ac o coooe oca poecco "poa" "y" ceoc oy.

paee (5.1) yoo epeca e x = r x(1- x k) (5.3) / e r = k =, paee (5.3) ec poco aeaeco oe, ya coca oopo ye oe o e eoopx aopo a cyy oy.

a o (5.1) (5.3), yeee ceoc x ac o copoc paoe oy a x. Mey e o eoe paee cpaeo ecoooo paoe. paooo oy ycox eopaex pecypco copoc paoe opeeec co cpe cao cao apao pace c poco ca ocoe x = r x2. (5.4) Oao oa ooc oy oe ea, o copoc paoe pyec ye e co cpe cao cao, a co cao oy. Oa ea apaa acoc copoc paoe ee eoopoe opaee p ox oocx yaec, a xx = a (5.5).

x opya (5.5) e ae peea poca ceoc oy e pecaae ee e p x oocx ceoc. Ho peax ycox oo aa pae oy, ec ceoc ee oycaec e eoopo peco e. Oeo, o cao c e, o p x oocx oy pe, eoxooe cpe oooope, caoc ye oe pee oeo oco, cocoo oooope. e o aop, e (5.5) e, oca cepoc, poopoay ceoc:

xx = a - x (5.6) x o ypaee ee a caoapx pee x1 = x2 = = l. (5.7) 0, - Aa oaae, o oa x1 = ycoa, a oa x2 = l eycoa. o ao oa cey opao. Ec aaa ceoc oy ee l(x < l), o oy poaec ee ceoc cpec y (x 0). Oao p x > l coaco (5.6) oy ye pac eopaeo. poopoa oy opeoo a oe ao a aee e peco e ee ceoc, e oopo oy eeo pae. Oaaoc, apep, o oy oyx o opeea a pae, o ee ooc ceac e peco e. o ecop a o, o oee oco cpeac Mpoo oeae, a oxoa a oyx o apeea. co ae, o peaa ceoc oy oa opaea cepxy, a a p ox oocx copoc paoe aae (e /x2 5.1) -a ypoo oype. Bpaee, yaee oa aopa pecy pay ceoc caoopaee p ox oocx, ee xx = a - x - x2. (5.8) x Ha pc. (5.1) oaa pa acoc ceoc o pee (a) copoc x(t) o ceoc x(t) ().

Ccea (5.8) ee ye p caoape o (cece oe caoapo ypae yx eo x3)) : x1 = (- x2 l x3 = K ycoe o = eycoa oa, pacooea a pae oace yx ycox peo ( l y apaepo ypae 5.8). B acoc o aao ceoc oy o pae: x 0 p x < l, o ocae acao a oooo ae coe ceoc (x ) p x >l.

a Pc. 5.1. acoc ceoc oy o pee (a) copoc poca o ceoc () cooec c opyo (5.8). pxoo ooaea oac poe oy oeo, ac pecaa cyy opeo oy, eoxoo apaee a e oo ee aay ceoc, o opee ye ae cepeo e l . B pe cyae yaec pee pee oy oaco pae, e oopo occaoee ceoc ye eooo, o ocoeo ao p apoa poco. Ec oe a oopaooe copaee ceoc pao oy, ee occaoee pocxo cpo (pa 1 pc. 5.1), e aaoo aaa, o peca oa ( ) ee aeo. aoopo, oee.aa occaoeo poecce (pa 3 pc. 5.1) oop o oaco oc pae eopaoo copae ceoc , ceoaeo, o eoxooc copa aca poca.

. B peax occeax poecc paoe e pocxo pae oe pee. o oaae, o ypaex copoc ee ceoc oy oa ace o e ceoc e o e, a pey oe pee. coa, o cce a eee e ee epeex pocxo e cpay, a epe e peeo epa T (aaae). B occeax o cao pee ceo c epoo aa oa pa oco. Ec pe pa poco oco cocae T, o ypaee, ocaee oe e ay ceoc pocx ocoe:

f ( ), ceye ae ypaee x = f (xt-T ), (5.9) e x ceoc ooopex ocoe oe pee t T.

t-T pyo e aaa pey ceoc ca c ceo xapaepo paoe ox o. B cyae, oa poce oco, paoaec ao oy, e oa o oo, o paoac ceye oy, ypaee c "o" aaae pe xn+ = f (xn), (5.10) e n ceoc oy oy n.

Caoopaee ceoc oy, yeoe (5.1) e apaoo ea ( x2), ocyecec peyae opae cpe poya eaoa, aaa. aop ac pee ceo o ceoc pocx ocoe, a oecy o aoee co a pae opace ca. o ae a, o opaee oe ceoc x a oe opeeec e a oy ocoe pey oe. C yeo x e ocecoe ypaee poca (5.1) epeec e x = x - x xt -T = x ( - xt -T ) (5.11) eco ypae poca (5.3) oy ecoe aeaeco oo ypaee Xacoa xt-T x r x - (5.12) = K e T opac ooo peoc.

Peee ypae c aaae pacpae paoopae aecx peo occeax , acoc, oaae yco ooe oea ceoc. Oa pa ooe oea ec a e, o ccee, peypyeo ee opao c, oopo pocxo cyecea aepa "opaeoo caa". o ee eco oy, e caoopaee ceoc x a oe t pocxo c aepo T o pee a ce eeeoc pocx ocoe pey oe t T. o ocoeo poec cceax, e pooeoc aep ee opao c peae coceoe xapaepoe pe cce. B occeax (5.11) (5.12) p T > 1/ (1/ coceoe pe > cce) oy oy apacae oea, xo ypaee e aaa ax oea ceoc e ae (c. pc. 5.1). B acoc o apaepo oea oy oc peyp epoec , aoopo, xaoec xapaep, p oopo acoa aya e oco. Ta coco oaa eoope oee aopaope occe.

Ha pc. (5.2) peea cepeaa pa oea ceoc yx o oyoo e. cceoae cooecye oe (pc. 5.3) oaao, o ooe eycooc apacax oea eoxoo, o pe pa o a o poco oco (aaae) o oe, e pe ececeo cep (T > 1/0). B pyx oex xaoecx oea o ycaoeo, o aya oepeo c ceoc po poopoaa epay ey ca (peyp xaoc). Booo, cyecoae cepxce aceox ppoe yaae a o, o aec pe ax oy "peyp xaoc".

Pc. 5.2. ceoc yx Lucilia C. oyoo e (Nicolson, 1954): I co pocx ocoe; II co , oaaex a e Pc. 5.3. aa ceoc oe -ao c aaae: acoxacecoe oeee Opooe paoopae cocoo aoec o eae, aaoc , eoo ocpoee ox oee, oopx opaac aooepoc poca oy ppoe. Oao acoc o oo, yeaec ocaec eeo ceoc oy ooo a pcyc pyoo oo accpoa aoec, e aac ea x exao. Cooeceo oy oxoy oe aoec o oy pex o:

1) oype o, eya yee ceoc oox o;

2) aoec a x-epa, oa yeee ceoc xa ( apaa) pocxo a ce yee ceoc ep (xoa);

3) co, ey yee ceoc oox o.

peoo, a o o ceao a pepe oe Boeppa x-epa, o eee ceoc (oacc) ooo yx o poopoao epooc cpe x ocoe, . e. poee x ceoce. Toa oo aca ypae, ocae aoec o c ceoc aoo x x cooeceo:

1 x = c x - a x a x x, (5.13) x = c x a x x - a x.

B x ypaex aaoo (5.1) ee e c x c x 1 1 2 2 oca coooe paoee o, a e (a x ) (a x ) 11 1 22 cooecy caoopae poca x oy. oee eo a x x a x x ao aoece o, xapaep oopoo y12 1 2 21 1 aec ao oeo. Ec oyppy, o oe opae a < 0, a < 0. p coe oa oea 12 ooe a > 0, a > 0. B cyae ooe x-epa o12 e a a e pae a.

12 Aa cce (5.13) a ycooc pooc c yeo ae ao oeo ypaex. M opac paccopee eoopx ocox peyao. B cyae oype ypae (5.13) py x1 = x1(c1 - a11x1 - a12x2 ), (5.14) x2 = x2(c2 - a21x1 - a22x2 ).

ppa y pae ac, ae, o ccea (5.14) oaae ep caoap oa, xapaep ycooc oopx oe ec acoc o ae oeo. Aa oaae, o oo oa oa cooecye ycooy cyecoa yx o p yco cpaeoc coooe ey oea,, <,, (5.15) 12 21 11 Bo cex ocax cyax o o eyco, o ycoe pe aac p yeo ceoc ooo o, . e. oa ae oo o .

Hepaeco (5.15) oaae, o oyppye oy cocyecoa ycoo ccee, ec poeee oeo eoyooo aoec,, ee, e poeee 12 oeo ypoyooo "caoopaeoo" aoec,,,. o oo eppepoa a opao, o 11 oaee ceoc ooo oypeo pocxo oe cee a ce caoopae p eo coceo poce, e a ce poca pyoo oypea. coa, peepo papocac oy caa opaae co poc, aa e ca oooc cyecoa cocee oy oypeo. Ececeo, o oe aac ooceo aopx ycox. B cypox e ycox, e pecypco e xaae "ce c y a opy c coepo", poc oy opae oe,,, a o cpa11 e c,,,. Toa epaeco (5.15) apyaec yco 12 pe caoc oo p a ooo caoo coo oypea. Ooe o a x-epa ye paccapac a a pepe oe Boeppa (c. . 2), e o oaao, o acoc o coooe apaepo ocoa oa cce (5.16) x1 x1(c1 a11x1 a12x2 ), (5.16) x2 x2 (c2 a21x1 a22x2).

oe o yco yo (p ox,,, ), o yco11 oyco. B aco cyae, oa oe, =0,, =0, 11 ccea oaae ocoo oo a ep (c. pc. 2.8). B o cyae oe caoc epyo e ae ycox eayxax oea, ocoy p o cyao yya ceoc ccea epexo c oo coao paeop a pyy c eee ay oea. Oao ppoe cepeax ycox aac ycoe oea ceoc , ceoaeo, ccee o cyecoa peyope exa coxpae oeaeoo coco, oope e ye cxoo oe (5.16).

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