Розробка та впровадження фрактальних методів аналізу хаотичних систем: Автореф. дис… канд. фіз.-мат. наук / П.В. Усік, НАН України. Ін-т радіофізики

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO ?AAe?IO?CEEE OA AEAEO?II?EE ?I. I. ss. ONEEIAA

On?e Iaaei A?eoi?iae/

OAeE 621.372.86: 621.373.4/.5

?IC?IAEA OA AI?IAAAeAEAIIss O?AEOAEUeIEO IAOIAe?A AIAE?CO OAIOE*IEO
NENOAI

01.04.03 — ?aae?io?ceea

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o ?aae?iano?iiii?/iiio ?inoeooo?

Iaoe?iiaeueii? Aeaaeai?? iaoe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Aaa??a Aeieo?i Ieoaeeiae/,

?aae?iano?iiii?/iee ?inoeooo IAI Oe?a?ie, i. Oa?e?a, caa?aeoth/ee
a?aeae?eii.

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Aooe A’y/aneaa Ieaenaiae?iae/, IIOe “Oa?e?anueeee o?ceei-oaoi?/iee
?inoeooo”, ?inoeooo ieaciaii? aeaeo?ii?ee oa iiaeo iaoiae?a
i?enei?aiiy; i. Oa?e?a, caa?aeoth/ee eaai?aoi???th;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, noa?oee iaoeiaee ni?a?ia?oiee Eoe?i
Einoyioei Ieaenaiae?iae/, ?inoeooo ?aae?io?ceee oa aeaeo?ii?ee ?i.
I.ss.Oneeiaa IAI Oe?a?ie, i. Oa?e?a, caa?aeoth/ee a?aeae?eii.

I?ia?aeia onoaiiaa: Oa?e?anueeee aea?aeaaiee oi?aa?neoao (eaoaae?a
oai?aoe/ii? ?aae?io?ceee), I?i?noa?noai ina?oe Oe?a?ie, i. Oa?e?a.

Caoeno a?aeaoaeaoueny » 21 » aeiaoiy 1999 ?. i 15.00 aiaeei? ia
can?aeaii?

niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.157.01 a ?inoeooo? ?aae?io?ceee oa
aeaeo?ii?ee ?i. I.ss. Oneeiaa IAI Oe?a?ie. (310085, i. Oa?e?a, aoe.
I?ineo?e,12)

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? I?A IAI Oe?a?ie.
(310085, i. Oa?e?a, aoe. I?ineo?e,12)

Aaoi?aoa?ao ?ic?neaiee » 20 » aa?aniy 1999 ?.

O. a. i. a/aiiai nae?aoa?y

niaoe?ae?ciaaii? a/aii? ?aaee

aeieoi? o?c.-iao. iaoe I.ss.Ee?e/aiei

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. No/ania ia?iaea aeaieo niinoa?aaeaiue iino?eii
aenoaa? iia? oa ana a?eueo neeaaei? aeiiae aei iaoiae?a, ui
aeei?enoiaothoueny aeey iaoeiaeo aeine?aeaeaiue. Oea iia’ycaii c?
ci?iith o inoaii? aeaaaeoeyoue ?ie?a oyae i?i i?e?iaeo aeaoa?i?iiaaiino?
oa aeiaaeeiaino? ? iio?aao? i?eioeeiiai iiaeo i?aeoiae?a aei ?ica’ycaiiy
oaeeo caaea/. Iiaa ?aea i?i oa, ui neeaaei?noue neaiaeo (iai?eeeaae,
oe?ieee niaeo?) ?ai?oa aaaaeaeanue iniiaiith i?eeiaoith iayaiino?
aaeeei? e?eueeino? nooiai?a naiaiaee aai i?enooiino? oaieiaeo oa ?ioeo
ooi?a. Oaia? anoaiiaeaii, ui neaiaee c aacia?a?aiei niaeo?ii iiaeooue
aooe ii?iaeaeai? aeaoa?i?iiaaieie ia’?eoaie c iaeei /eneii nooiai?a
naiaiaee, aeeiai?ea yeeo, iaeiae, ? oaioe/iith. Oaioe/i? i?ioeane
iaoiiaeai? aeeiai?eith nenoai iaei? ?ici??iino?, ye? iienothoueny
cae/aeieie aeeoa?aioe?aeueieie aai ??cieoeaaeie ??aiyiiyie iaaenieiai
ii?yaeeo.

E?ioeaaith iaoith i?e ia?iaoe? aeaieo niinoa?aaeaiue, ye? yaeythoue
niaith ?a?no?aoe?? aeayeeo neaiae?a, ? aeae?eaiiy neeaaeo oa?aeoa?ieo
aeanoeainoae, ye? aeicaieythoue c?iaeoe aeniiaee i?i ia’?eo, ui ?
aeaea?aeii oeeo neaiae?a, oa iiaoaeoaaoe, ia iniia? oeueiai, eiai
oaiiiaiieia?/io aai iaoaiaoe/io iiaeaeue. Aeei?enoaiiy noaiaea?oieo
iaoiae?a ei?aeyoe?eiiai oa niaeo?aeueiiai aiae?co aeey nenoai c
oaioe/iith iiaaae?ieith ia aeicaiey?, ii-ia?oa, a?ae??cieoe ?o a?ae
ooiiaeo, a ii-ae?oaa, i?iaanoe ?o eeaneo?eaoe?th. Iaeiei c iiaeeeaeo
i?aeoiae?a aei ?ica’ycaiiy caaea/ c ?aeaioeo?eaoe?? oa eeaneo?eaoe??
neeaaeieo neaiae?a, ye? aaia?othoueny e?ioeaaii??ieie iae?i?eieie
nenoaiaie, ? aecia/aiiy oa?aeoa?enoee, ye? iathoue iacao o?aeoaeuei?
?ici??iino?. C oa?aeoa?enoee oaeiai oeio, aeine?aeieee iaeoe?oa,
aeei?enoiaothoue ei?aeyoe?eio ?ici??i?noue, oi/a ?iiae? ciaoiaeyoue
canoinoaaiiy oa ?io? oeie ?ici??iinoae. Oaeiai ?iaeo ?ic?aooiee
aeicaieythoue ioe?ieoe aoaeoeaia /enei nooiai?a naiaiaee nenoaie, yea
aaia?o? neaiae, ui i?eioeeiiai iaiao?aeii aeey iiaoaeiae ?? aaeaeaaoii?
iaoaiaoe/ii? iiaeae?. Ciai?oiy i?inoioa ?ic?aooie?a coiiaeea ia?aaaao o
aeei?enoaii? ei?aeyoe?eii? ?ici??iino? o ii??aiyii? c ae?oaeie
oa?aeoa?enoeeaie ?ici??iiniiai oeio, ?ic?aooiee yeeo, oaeiae,
i?eioeeiiai aeicaieythoue ?ica’ycoaaoe oeacai? caaea/?. Ii?yae c oei,
a?eueo ?aoaeueia aea/aiiy oi/iino?, iaae?eiino? oa ca?aeiino?
i?ioeaaeo?e ?ic?aooie?a c o?aooaaiiyi aeieeath/eo i?e oeueiio
nenoaiaoe/ieo oa noaoenoe/ieo iioeaie, iieacaei, ui aeei?enoaiiy oaei?
oaoi?ee iio?aao? cia/ii? iaa?aaeiino? oa aeaaeeeaino? o aeai??
ia?aiao??a.

Aei ii/aoeo i?iaaaeaiiy aaoi?ii oeeo aeine?aeaeaiue i?aeoe/ii ia aoei
aea/aii ieoaiiy i?i iiaeeea?noue aeei?enoaiiy oaeiai iaoiaeo ia?iaee aei
neaiae?a c ?ici??i?noth aeua i?ae 3, ye? caciathoue aieeao nioaiai?
o?eueo?aoe??. Iinoaiiaa oaei? caaea/? coiiaeaia oei, ui i?aeoe/ii an?
neaiaee, ye? ?a?no?othoueny, iniaeeai a ?aae?io?ceoe?, caciathoue oaeiai
?iaeo ia?aoai?aiue o i?eeiaeueieo i?eno?iyo. Oiio ieoaiiy i?i
a??ia?aei?noue io?eiaieo ?acoeueoao?a aeey oaeeo neaiae?a aeiaaaei
iaaaeiiai oa aeeaieiai aea/aiiy, ui ? aoei c?iaeaii a aeai?e ?iaio?.

Iaei??th c iaeaaaeeea?oeo iaoith aeine?aeaeaiue oaioe/ieo yaeu ?,
aacoiiaii, i?aeoe/ia aeei?enoaiiy oaeeo eieeaaiue a oaoi?/ieo i?eno?iyo.
Oeueiio iai?yieo i?enay/ai? aeine?aeaeaiiy c iiaeaeueoiai ?icaeoeo
iiaiai i?aeoiaeo a eiaeoaaii?-aeaeiaeoaaii? ?ioi?iaoe??, aeei?enoiaoth/?
oaioe/ia eieeaaiiy, ye iin?e ei?eniiai neaiaeo. Oeae i?aeo?ae
a?ae??ciy?oueny a?ae ?ioeo, a?aeiieo ia oeae /an, oei, ui ia
aeei?enoiao? yaeua oaioe/ii? neio?ii?caoe??.

Aeooaeuei?noue oaie coiiaeaia oaeiae ?ioa?anii, yeee a inoaii?e /an
aeyaeythoue iaoeiaoe? aei oaeiai ?iaeo aeine?aeaeaiiue. ?ic?iaea oa
aaeineiiaeaiiy iiaeo iaoiae?a aiae?co aeaieo niinoa?aaeaiue ?
aeooaeueiei ? aaaeeeaei iai?yieii iaoeiai-aeine?aeieo ?ia?o. Oae?
iaoiaee iiaeia aeei?enoiaoaaoe aeey ia?iaee aeaieo i?e i?iaaaeaii?
?aae?io?ce/ieo, ano?iiii?/ieo oa ano?io?ce/ieo aeine?aeaeaiue, ui
aeooaeueii ? a Oe?a?i? oaeiae.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie oa oaiaie. Ci?no
aeena?oaoe?eii? ?iaioe ? /anoeiith oai?aoe/ieo oa aenia?eiaioaeueieo
aeine?aeaeaiue, ye? i?iaiaeeeenue a ?aae?iano?iiii?/iiio ?inoeooo?
Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie a 1992-1998 ?ieao. Na?aae ieo oae?
ye:

“Aeeiai?/iee oain a iae?i?eieo eieeaaeueieo nenoaiao oa iia? iaoiaee
aiae?co aeaieo niinoa?aaeaiue a ano?io?ceoe?”, Oeo? “Aeeiai?ea”, (iiia?
aea?ae?a?no?aoe?? 0197U 19098),

i?iaeoe Aea?aeaaiiai oiiaeo ooiaeaiaioaeueieo aeine?aeaeaiue:

-“Oaioe/ia aeeiai?ea ano?io?ce/ieo ia’?eo?a oa o?aeoaeuei? iaoiaee
ia?iaee neaiae?a” Oeo? “Naaeei” (iiia? aea?ae?a?no?aoe?? 0193U 009125);

-“Aeine?aeaeaiiy aeeiai?/ieo oa?aeoa?enoee i?ioean?a aia?aiaeae?eaiiy ia
Niioe?” Oeo? “Ei?iia” (iiia? aea?ae?a?no?aoe?? 0193U 009127);

-“Aeeiai?/iee oain a i?ioeanao i?aeneeaiiy, aaia?aoe?? oa ia?aoai?aiiy
aeaeo?iiaai?oieo oa a?ae?iaeeiai?/ieo oaeeue” ?2.4/296;

a oaeiae i?ia?aie, ye? i?aeo?eiai? I?aeia?iaeiei iaoeiaei oiiaeii.

Iaoa ? caaea/? aeine?aeaeaiiy iieyaathoue o:

· ?ic?iaoe? oa aeei?enoaii? iaoiaeeee ioe?iee nenoaiaoe/ieo oa
aeiaaeeiaeo iioeaie i?e i?iaaaeaii? ?ic?aooie?a ei?aeyoe?eii?
?ici??iino? ca aeaieie niinoa?aaeaiue;

· aecia/aii? e?eoa???a iioeiaeueiiai aeai?o ea?oaaeueieo ia?aiao??a
oaei? i?ioeaaeo?e;

· iaa?oiooaaii? aeei?enoaiiy iaoiaeeee ?ic?aooieo ei?aeyoe?eii?
?ici??iino? aei neaiae?a, ye? ao?aoeee aiane?aeie o?eueo?aoe?? /anoeio
nioae oa?aeoa?ieo /anoio;

· aiae?c? i?aoeacaeaoiino? noai eiaeoaaiiy – aeaeiaeoaaiiy ?ioi?iaoe??,
aaciaaieo ia aaoiiiiiiii?e nenoai? ?ueinea?a oa iaaaoiiiiiiio ??aiyii?
iayoieea, ia aeei?enoiaoth/? yaeua oaioe/ii? neio?ii?caoe??;

· ?ic?iaoe? aoaeoeaieo cania?a iicaaaeaiiy a?ae ooi?a o oeeo noaiao.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a:

· ?ic?iaeaii iaoiaeeeo ioe?iee nenoaiaoe/ieo oa aeiaaeeiaeo iioeaie i?e
i?iaaaeaii? ?ic?aooie?a ei?aeyoe?eii? ?ici??iino? ca aeaieie
niinoa?aaeaiue;

· aaeineiiaeaii iaoiaeeeo aeai?o iioeiaeueieo ia?aiao??a i?ioeaaeo?e
?ic?aooie?a, oaeeo ye iaae? oa aeiaaeeia neaee?iaiaiai ?ioa?aaeo,
e?euee?noue oi/ie, o?eaae?noue ?aae?caoe?? oa ?o ca’ycie c a?aeiioaiiyi
neaiae/ooi,

· aia?oa aeine?aeaeaii aieea nioaiai? oeeueo?aoe?? ia ioe?ieo
ei?aeyoe?eii? ?ici??iino? aeey neaiae?a c ?ici??i?noth aeua i?ae 3 oa
io?eiaii e?euee?ni? ioe?iee aee?eaeaiue aeey ?aeaaeueiiai o?eueo?o oa
oeeo?iaiai o?eueo?o ae?oaiai ii?yaeeo;

· aia?oa iaa?oioiaaii aeei?enoaiiy iaoiaeeee ?ic?aooieo ei?aeyoe?eii?
?ici??iino? aei neaiae?a, ye? aiane?aeie nioaiai? o?eueo?aoe?? ao?aoeee
/anoeio nioae oa?aeoa?ieo /anoio;

· aia?oa aeei?enoaia iaoiaeeea ioe?iee ei?aeyoe?eii? ?ici??iino? aeey
aiae?co aeaieo niinoa?aaeaiue i?e?naeoiaeieo ioeuenaoe?e niiy/iiai
?aae?iaei?ii?ithaaiiy a ae?aiacii? /anoio 2.5 oa 2.85 AAoe;

· cai?iiiiiaaii noaie iicaaaeaiiy a?ae ooi?a i?e aeei?enoaii?
aeaoa?i?iiaaiiai oaino o caaea/ao eiaeoaaiiy oa aeaeiaeoaaiiy
?ioi?iaoe??, ye? ia aacothoueny ia yaeu? oaioe/ii? neio?ii?caoe?? oa
io?eiaii e?euee?ni? ioe?iee aieeao ia?aiao??a noaie ia ye?noue
ianeoaaiiy oa a?aeiiaeaiiy neaiaeo, ui ia?aaea?oueny.

Iaa?oioiaai?noue oa aeinoia??i?noue iaea?aeaieo a ?iaio? ?acoeueoao?a
aecia/a?oueny aaeaeaaoi?noth aeei?enoaieo oai?aoe/ieo iiaeaeae ?aaeueiei
o?ce/iei oiiaai, ei?aeoi?noth canoiniaaieo iaoaiaoe/ieo iaoiae?a
aiae?oe/iiai oa /enaeueiiai aiae?co, i?aeoaa?aeaeo?oueny ii??aiyiiyie c
?acoeueoaoaie, ye? aoei io?eiaii ?ai?oa ae?oaeie aaoi?aie.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?acoeueoaoe ?iaioe, ye?
aeeeaaeai? o ae?oaiio oa o?aoueiio ?icae?eao, iiaeooue aooe oe?iei
aeei?enoai? aeey aeine?aeaeaiue aenia?eiaioaeueieo aeaieo aoaeue-yei?
i?e?iaee aeey aeyaeaiiy oa aiae?co oaioe/ieo yaeu o ?aae?io?ceoe?,
?aae?iano?iiii??, ano?io?ceoe?, a?ieia??, o?i?? oa ?ioeo aaeocyo iaoee,
ye? iathoue ni?aae c ia?iaeith aeaieo, ui aeaeyaeathoue ye /enaeuei?
ianeae c o?eniaaiei /anii aeai?ee. ?acoeueoaoe aeine?aeaeaiue, ye?
?icaeyiooi o /aoaa?oiio ?icae?e?, iiaeooue aooe aeei?enoai? aeey
noai?aiiy oaoi?/ieo i?eno?i?a eiaeoaaiiy oa aeaeiaeoaaiiy ?ioi?iaoe??, o
yeeo iin??i ?ioi?iaoe?? aoaeooue oaioe/i? eieeaaiiy.

Iniaenoee aianie caeiaoaa/a a ?iaioe, ye? iaienai? o ni?aaaoi?noa?,
iieyaa? a o/ano? o iinoaiiaoe? caaea/ [2,3,6], ae??oaii? iinoaaeaieo
caaea/; ?ic?iaoe? /enaeueieo aeai?eoi?a, i?iaaaeaii? ?ic?aooie?a oa
aiae?c? iaea?aeaieo ?acoeueoao?a [1-6]. A ioae?eaoe?? [2] aaoi?o ia
iaeaaeaoue i?ae?icae?ee, a yeeo i?iaaaeaii aiae?c aeaieo c aeei?enoaiiyi
aaeaeaoieo ia?aoai?aiue.

Ia caoeno aeiinyoueny oae? ?acoeueoaoe, io?eiai? aaoi?ii:

1.Ioe?iea oi/iino? ?ic?aooie?a ei?aeyoe?eii? ?ici??iino? ca aeaieie
niinoa?aaeaiue ? iaoiaeeea aeai?o iioeiaeueieo ia?aiao??a i?ioeaaeo?e
?ic?aooie?a.

2. Aeieac iiaeeeaino? ?ic?aooieo ei?aeyoe?eii? ?ici??iino? neaiae?a, ye?
caciaee aieeao nioaiai? o?eueo?aoe??.

3. ?acoeueoaoe ?ic?aooieo ei?aeyoe?eii? ?ici??iino? aeey aeaieo
niinoa?aaeaiue i?e?naeoiaeieo ioeuenaoe?e niiy/iiai
?aae?iaei?ii?ithaaiiy a ae?aiacii? /anoio 2.5 oa 2.85 AAoe;

4. Ioe?iee yeino? aeaeiaeoaaiiy ?ioi?iaoe?? o ianeio?ii?ciaaieo
aaoiiiiieo oa iaaaoiiiiieo eieeaaeueieo nenoaiao c oaioe/iith
iiaaae?ieith.

5. Caniae iicaaaeaiiy a?ae ooi?a o nenoaiao i?eoiaaiiai ia?aaeaaaiiy
?ioi?iaoe??, ye? aeei?enoiaothoue ianeio?ii?ciaai? oaioe/i? nenoaie.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Aeeeaaeai? a aeena?oaoe?ei?e
?iaio? iaoeia? ?acoeueoaoe iaaiai?thaaeeny ia XVII I?aeaaeocaa?e
iaoeiai-oaoie/i?e eiioa?aioe?? “Iaoiaee oa i?eno?i? ia?iaee
?aae?ieieaoe?eii? ? ?aae?ioaoi?/ii? ?ioi?iaoe??” (i. Ee?a, 1992?.) [5],
ia I?aeia?iaei?e eiioa?aioe?? “Applied nonlinear dynamics and stochastic
systems near the millenium” (Nai-Ae??ai, NOA, 1997?.) [6], oa ia
iaoeiaeo nai?ia?ao ?? IAI Oe?a?ie.

Ioae?eaoe?? : 3 noaoo? a iaoeiaeo aeo?iaeao [1-3], 1 oace aeiiia?aeae ia
eiioa?aioe?? [5], 1 iaoa??aee i?aeia?iaeii? eiioa?aioe?? [6] oa 1
i?ai?eio [4].

No?oeoo?a oa ianya aeena?oaoe??. Iniiaiee oaeno aeena?oaoe??
neeaaea?oueny ?c anooio, /ioe?ueio ?icae?e?a ? aeniiae?a (135 noi??iie
iaoeiiieniiai oaenoo). ?iaioa i?noeoue 42 ?ethno?aoe?? ? aeeth/a? nienie
e?oa?aoo?e, ui neeaaea?oueny c 102 a?ae?ia?ao?/ieo iaeiaioaaiue ia 10
noi??ieao. Caaaeueiee ianya ?iaioe 149 noi??iie.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie oa i?eeeaaeia cia/aiiy
aeena?oaoe??. Aeeeaaeaii ca’ycie ?iaioe c iaoeiaeie ieaiaie ? i?ia?aiaie
??IAI Oe?a?ie. Noi?ioeueiaaii iaoo ?iaioe, i?eaaaeaii ei?ioeee ci?no oa
iniiai? iieiaeaiiy, ui aeiinyoueny ia caoeno, a oaeiae iaa?oioiaaii
iaoeiao iiaecio oa i?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a.

A ia?oiio ?icae?e? ?icaeyiooi e?oa?aoo?o c i?iaeai, ui ?ica’ycothoueny o
aeena?oaoe?ei?e ?iaio? oa ie?aneaii noai ieoaiue, ye? aoaeooue ae??oai?.
Na?aae ieo i?eae?eaii oaaao aeueoa?iaoeaiei iaoiaeai ioe?iee e?eueeino?
nooiai?a naiaiaee aeeiai?/ieo nenoai, cie?aia ?icaeyiooi ?iceeaaeaiiy
neaiaeo ia iaei?aeueiaai? eiiiiiaioe. Aea/aii aeaye? ?nioth/? oai?aoe/i?
iiaeae? ?aae?iaei?ii?ithaaiiy niiy/ieo niaeao?a o i?e?iao?iaiio
ae?aiacii? aeiaaeei oaeeue oa ?acoeueoaoe aiae?co aeeiai?/ieo
aeanoeainoae oaeiai aei?ii?ioaaiiy. Aeine?aeaeaii ?nioth/? noaie
neio?ii?ciaaieo oaioe/ieo nenoai, iiaeeea?noue ?o aeei?enoaiiy aeey
oe?eae i?eoiaaiiai ia?aaeaaaiiy ?ioi?iaoe?? oa aecia/aii iaaeie?ee ?
ia?aaaae oaeeo noai.

Ae?oaee ?icae?e “Aiae?c aenia?eiaioaeueieo aeaieo ca aeiiiiiaith ioe?iee
o?aeoaeueii? ?ici??iino?” aeena?oaoe?? i?noeoue ?icaeyae iaoiaeeee
?ic?aooieo o?aeoaeueii? ?ici??iino? oa aeai?o iioeiaeueieo ea?oaaeueieo
ia?aiao??a oe??? i?ioeaaeo?e. Aea?oueny icia/aiiy ei?aeyoe?eii?
?ici??iino? oa cania?a ?? ioe?iee. Noi?ioeueiaaii caaaeueio noaio
?ic?aooie?a ei?aeyoe?eii? ?ici??iino?, yea i?noeoue /ioe?e iniiai?
aoaie.

1)Iiia?aaeiy ia?iaea aeaieo. Ia oeueiio aoai? canoiniaothoue ioe?ieo
Oo?ue?-niaeo?a ? ?iceeaaeaiiy neaiaeo ia iaei?aeueiaai? eiiiiiaioe.

2)Iiaoaeiaa n-i??iiai aaeoi?iiai neaiaeo wmetafile8?
??N???????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????Ayyy?yyy`??T?? ???&?
?MathType??`????u`th??????

wmetafile8? ??Ue???????????
???????????yyy????.????1?????? ??????? 
`%???&??yyyy?????Ayyy!yyy %??A?? ???&?
?MathType?? ????u@th??????

3)?ic?aooiie ei?aeyoe?eiiai ?ioaa?aeo Cn(r) o i?inoi?ao ??cieo
?ici??iinoae n. Oi?ioea ?ic?aooieo ia? oaeee aeaeyae.

wmetafile8? ??1???????????
???????????yyy????.????1?????? ???????  @

???&??yyyy?????Ayyyµyyy?

??O?? ???&? ?MathType?? 
???u?????????»????-?????pAE???p? ???uAth??????

aea N-e?euee?noue oi/ie, (…) — ooieoe?y Oaa?naeaea, r- a?aenoaiue i?ae
oi/eaie, wmetafile8? ??1/2????????????
???????????yyy????.????1?????? ??????? ?  ???&?
?MathType??P????u????????????-????? ?^????U^????
?(????U(???? ?e???Ue???
?????U????`r????u?th??????

wmetafile8? ??o???????????
???????????yyy????.????1?????? ???????
AA???&??yyyy?????Ayyy?yyy???o?? ???&? ?MathType??
???u?????????»????-?????ax ???~x
???aB???~B???u?th??????

aea -iiceoeaia /enei,(yeui =2, oi ii?ia-aaee?aeiaa a?aenoaiue) yik —
k-oa eii?aeeiaoa i-i? oi/ee.

4) C’ynoaaiiy cia/aiiy . I?e oeueiio ne?ae aecia/eoe oaiaain eooa
iaeeiio o eii?aeeiaoao log[Cn(r)] — log(r).

?icaeyiooi ieoaiiy aeai?o aeai?eoio ?ic?aooie?a ei?aeyoe?eiiai
?ioaa?aeo, yea ? ae??oaeueiei aeey c’ynoaaiiy iio?aae eiiiuethoa?iiai
/ano ?iaioe i?ia?aie.

O i?ae?icae?e? 2.4. ae??oaii ieoaiiy iioeiaeueiiai aeai?o /ano cao?eiee
, aeaaaeaii ca’ycie c a?aeiioaiiyi neaiae/ooi oa c’yniaaii o?eueo?oth/?
aeanoeaino? i?ioeaaeo?e ?ic?aooie?a. Aeaaaeaii oi?ioee aeey ieaeiuei?
Oe?1 oa aa?oiuei? Oe?2 iaae? ia?aiao?a .

wmetafile8? ??o???????????
???????????yyy????.????1?????? ???????
?A???&??yyyy?????Ayyy·yyy???·?? ???&? ?MathType??

aea Oo-oa?aeoa?iee /an, q – a?aeiioaiiy neaiae/ooi, n-?ici??i?noue
aeeaaeaiiy.

Ianooiiee i?ae?icae?e aena?oeth? iniiai? aeaea?aea iioeaie i?e
?ic?aooieao ei?aeyoe?eii? ?ici??iino? . Aeae?eaii o?e iniiai? oaeoi?e,
ye? i?eaiaeyoue aei iaoi/iinoae i?e ?? ?ic?aooieao:

1)noaoenoe/iee oa?aeoa? ei?aeyoe?eiiai ?ioaa?aeo;

2)aieea iaae ia’?eoo;

3)eaeoia?i?noue o?aeoaeueieo iiiaeei.

Canoiniaoth/e iiaeaeue a?ia?eoaa aeaaaeaii ae?ace aeey aeiaaeeiaeo
iioeaie ei?aeyoe?eiiai ?ioaa?aeo C

wmetafile8? ??ss???????????
???????????yyy????.????1?????? ???????
  ???&??yyyy?????Ayyy?yyy`??O?? ???&? ?MathType??

aea N — e?euee?noue oi/ie, r- a?aenoaiue i?ae oi/eaie, tp — ia?aiao?
eiia??i?niiai ?iciiae?eaiiy; oa eiai nenoaiaoe/ieo iioeaie.

wmetafile8? ??o???????????
???????????yyy????.????1?????? ???????
?`???&??yyyy?????Ayyy§yyy ??’?? ???&? ?MathType??
???u?????????»????-?????e???%t
????J????Oe???u?th??????

aea A[…]-aaiia-ooieoe?y.

I?e oeueiio nai ei?aeyoe?eiee ?ioaa?ae ia? oaeee aeaeyae:

wmetafile8? ??a???????????
???????????yyy????.????1?????? ??????? a
???&??yyyy?????Ayyyµyyya??•?? ???&?
?MathType??????u@th??????aea wmetafile8? ??™???????????
???????????yyy????.????1?????? ???????
?a$???&??yyyy?????Ayyy©yyy $??)?? ???&? ?MathType??
???u?????????»????-??????u????????i?7????©???W
?)????j

???foe???&g?????????$???u@th??????

Caaaeueio iioeaeo i?e ?ic?aooieao ei?aeyoe?eii? ?ici??iino? aeey
?ici??iino? aeeaaeaiiy n iiaeia ioe?ieoe ii oae?e oi?ioe?:

wmetafile8? ??”???????????
???????????yyy????.????1?????? ???????
  (???&??yyyy?????Ayyy±yyy`(??Q?? ???&? ?MathType??0
???u?????????»????-??????0????a???I?!???

I?e oeueiio ia?oee /eai iieno? nenoaiaoe/io, a ae?oaee aeiaaeeiao
neeaaeiao /anoeio iioeaee.

?icaeyiooi aca?iica’ycie e?eueeino? oi/ie oa neaee?iaiaiai ?ioa?aaeo.
Iieacaii ca’ycie i?ae ?ici??i?noth aeeaaeaiue i oa iioeiaeueiith
aeiaaeeiith neaee?iaiaiai ?ioa?aaeo kiio

wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyy?yyy`????? ???&?
?MathType??`????u@th??????

Iaaaaeaii a?ao?ee caeaaeiinoae kiio a?ae /enea nooiai?a naiaiaee n
(?en.1), ieaeiuei? iaaee neaee?iaiaiai ?ioa?aaeo r1oio a?ae e?eueeino?
oi/ie N aeey ??cieo ?ici??iinoae aeeaaeaiue i (?en.2), oa caeaaeiino?
iioeiaeueieo ia?aiao??a a?ae ??aith ooi?a (?en.3.). Iioeiaeueia cia/aiiy
ieaeiuei? iaae? neaee?iaiaiai ?ioa?aaeo aecia/a?oueny oi?ioeith (10)

?en. 1. Caeaaei?noue iioeiaeueieo cia/aiue aeiaaeeie neaee?iaiaiai
?ioa?aaeo Eoptr1/r2 (e?eaa 1) e kopt Cn(r1)/Cn(r2) (2) a?ae ?ici??iino?
i?inoi?o aeey iiaeae? a?ia?eoaa.

?en. 2. Caeaaei?noue iioeiaeueieo cia/aiue ieaeiuei? a?aieoe?
neaee?iaiaiai ?ioa?aaeo r1ipt a?ae e?eueeino? oi/ie N i?e ??cieo n aeey
iiaeae? a?ia?eoaa. E?i?? 15 a?aeiia?aeathoue n = 3, 5, 7, 9, 11.

?en. 3. Caeaaei?noue cia/aiiy iioeaee n a?ae ni?aa?aeiioaiiy neaiae/ooi
aeey iiaeae? a?ia?eoaa i?e N = 105. E?ea? 14 a?aeiia?aeathoue n = 3, 7,
9, 11.

wmetafile8? ??A???????????
???????????yyy????.????1?????? ???????
 a???&??yyyy?????Ayyy?yyy ??_?? ???&? ?MathType??P
???u?????????»????-?????aea wmetafile8? ??‘???????????
???????????yyy????.????1?????? ???????
@A???&??yyyy?????Ayyy±yyy???n?? ???&? ?MathType??
???u?????????»????-??????????oz ??? ????yY
???u?????????»????-?????Y???®A???-?????®A???n¦
???n¦???nA???°z???°=???

Oaeiae i?eae?eaii oaaae aiae?co ?ioeo iaoiae?a aecia/aiiy iieacieea ,
yeee aecia/a? cia/aiiy ei?aeyoe?eii? ?ici??iino?. O i?ae?icae?e?
“Aeiaaeeia ?aae?caoe??” iaaeaii ?aeiiaiaeaoe??, uiaei aeai?o iaiao?aeii?
e?eueeino? aeaieo oa /anoioe ?o aea??ee ca /anii aeey iiaeaeueoiai
i?iaaaeaiiy ?ic?aooieo ei?aeyoe?eii? ?ici??iino?. Caaa?oo?ony oeae
?icae?e caaaeueieie ?aeiiaiaeaoe?yie ii i?iaaaeaiith aenia?eiaio?a, aea
c?iaeaii i?aenoiie ?acoeueoaoai, ye? io?eiai? o ae?oaiio ?icae?e?.

O?ao?e ?icae?e i?enay/aii ?icaeyaeo iaoaiaoe/ii? iiaeae? i?ioiaeaeaiiy
neaiaea e??cue i?eeiaeueiee i?eno??e, aeine?aeaeaiith iiaeeeaino?
ioe?iee ei?aeyoe?eii? ?ici??iino? i?ney i?ioiaeaeaiiy neaiaea e??cue
o?eueo?e, i?iaiae?ciaaii aieea, yeiai caaaeathoue ??ci? oeie o?eueo??a
ia aeeiai?eo ao?aeiiai neaiaea. Oaeiae aeine?aeaeaii aieea ia?aiao??a
nioaiaiai o?eueo?o ia ioe?ieo ei?aeyoe?eii? ?ici??iino? aocueeinioaiaeo
oa oe?ieinioaiaeo neaiae?a, ui i?eeiathoueny aioaiaie. ?acoeueoaoe
?ic?aooie?a iaaaaeaii o aeaeyae? a?ao?e?a a?aeiia?aeieo caeaaeiinoae,
ye? /anoeiai i?eaaaeai? ia ?en.4 oa ?en.5.

?en. 4. Caeaaei?noue cia/aiue ei?aeyoe?eii? ?ici??iino? oe?ieinioaiaiai
neaiaea, yeee i?ieoia e??cue ?aeaaeueiee oeeo?iaee o?eueo?, a?ae
oeaio?aeueii? /anoioe o?eueo?o aeey ??cieo cia/aiue oe?eie nioae
i?iioneaiiy o?eueo?o.

?en. 5. Caeaaei?noue cia/aiue ei?aeyoe?eii? ?ici??iino? aocueeinioaiaiai
neaiaea, yeee i?ieoia e??cue oeeo?iaee o?eueo? ae?oaiai ii?yaeeo, a?ae
oe?eie nioae i?iioneaiiy o?eueo?o aeey ??cieo cia/aiue oeaio?aeueii?
/anoioe o?eueo?o.

E??i oeueiai a aeaiiio ?icae?e? ?icaeyiooi canoinoaaiiy iaoiaeeee
?ic?aooieo ei?aeyoe?eii? ?ici??iino? aei aeaieo niinoa?aaeaiue. sse
i?eeeaae aeaieo niinoa?aaeaiue aea?aii caiene ?aae?iaei?ii?ithaaiiy naie
niiy/ieo ?aae?iniaeao?a, ye? aoee cao?eniaai? ia E?einuee?e
Ano?io?ce/i?e Iana?aaoi??? (E?AI) ia /anoioao 2.5 e 2.85 AAoe c
i?e?naeoiaeiei ?icae?eaiiyi ca /anii. ?ioi?iaoe?th i?i aeai?, ye? aoei
i?iaiae?ciaaii caaaeaii o oaaeeoeth.

Oaaeeoey. Ia?ae?e iiae?e, ui i?iaiae?ciaaii.

?.AeaoaE?euee?noue oi/ie *anoioa (AAoe)Ii/aoie o?aaiaioo (UT)E?iaoeue
o?aaiaioo (UT)*anoioa aeene?ao.
(Aoe)189/03/12250002.8508:17:3608:20:50125289/09/01124312.8506:16:5207:1
0:00125389/10/1931252.8512:48:3413:15:00115490/02/1245002.8508:50:5208:5
1:26125591/11/17263872.5, 2.8507:04:0507:07:37111691/04/16174002.5,
2,8511:41:2611:44:00113791/04/16334002.5, 2.8511:49:0111:53:57113

Ca ?acoeueoaoaie ia?iaee oeeo ?aae?caoe?e i?iaaaeaii aiae?c iaoai?cio
aeieeiaiiy i?e?naeoiaeieo ioeuenaoe?e ?aae?iaei?ii?ithaaiiy Niioey ?
iieacaii, ui oae? i?ioeane ia iathoue iecueei?ici??ii? aeaoa?i?iiaaii?
i?e?iaee.

Ci?no /aoaa?oiai ?icae?eo neeaaea? aiae?c iaoiaeo i?eoiaaiiai
ia?aaeaaaiiy ?ioi?iaoe??, caniiaaiee ia ?iaa?ooaaii? oaioe/ieo
aeeiai?/ieo nenoai a?aeiinii ?ioi?iaoe?eiiai neaiaeo, yeee aeiaea?oueny
a ii/aoeia? aeeoa?aioe?aeuei? ??aiyiiy. Oeae i?aeo?ae, ia a?aei?io a?ae
a?aeiieo ?ai?oa, ia iio?aao? aeei?enoaiiy oaioe/ii? neio?ii?caoe?? aeaio
aai a?eueoi? e?eueeino? inoeeeyoi??a. Iaaaaeaii aiae?c iaaeie?e?a aeaio
a?oi noai, ye? aoei cai?iiiiiaaii ?ai?oa. Aeine?aeaeaii aieea ooi?a o
eaiae? ca’yceo oa ?ica?aeiino? ia?aiao??a inoeeeyoi??a ia ye?noue
aeaeiaeiaaiiai neaiaeo, cai?iiiiiaaii caniae cieaeaiiy ooi?a o
aeo?aeiiio neaiae?. sse i?eeeaaee ia?aaeath/eo noaie aeei?enoaii
aaoiiiiiee inoeeeyoi? ?ueinea?a oa iaaaoiiiiia ??aiyiiy iayoieea.
A?aeiiaeaiiy ?ioi?iaoe?eiiai neaiaeo c nenoaie ?ueinea?a cae?enith?oueny
ca oi?ioeith (11).

wmetafile8? ??e???????????
???????????yyy????.????1?????? ??????? 
`,???&??yyyy?????Ayyy¶yyy ,??Oe?? ???&? ?MathType??P???u1/4y
????aea a,b,c — ia?aiao?e nenoaie ?ueinea?a, o=o(t) — ci?iia, ui
ia?aaea?oueny eaiaeii ca’yceo, i(t) — ?ioi?iaoe?eiee neaiae.

Aeey oaei? noaie cai?iiiiiaaii iaoiaeeeo iicaaaeaiiy a?ae aaeeoeaieo
ooi?a eaiaeo, yea iieyaa? a iieaneaaeiiio caeaaeaeoaaii? aeo?aeiiai
neaiaeo ia?aae eiaeiei aeeoa?aioe?thaaiiyi ca aeiiiiiaith o?eueo?o
ieae/eo /anoio. ?icaeyiooi i?aeo?ae aei aeai?o oaeiai o?eueo?o, oa eiai
aoaeoeai?noue.

Aeey a?aeiiaeaiiy ?ioi?iaoe?eiiai neaiaeo o noai? c aeei?enoaiiyi
??aiyiiy iayoieea cai?iiiiiaaii oi?ioeo (12)

wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
?`(???&??yyyy?????Ayyy®yyy (??.?? ???&? ?MathType?????u»y
????

aea x*(t)- aeia?eueia ??oaiiy aeey ocaaaeueiaii? oace iayoieea, ui
ia?aaea?oueny eaiaeii ca’yceo, — aeanoeaa /anoioa, wmetafile8?
??…???????????? ???????????yyy????.????1??????
??????? ``???&??yyyy?????Ay ? ? ???&?
?MathType??0????u?th??????O oae?e noai? i?iiiio?oueny iinooiiaa
a?aeiiaeaiiy ia a?ae?aco ?ioi?iaoe?eiiai neaiaeo i(t), a nii/aoeo eiai
noie c ciai?oiith neeith:

wmetafile8? ??A???????????
???????????yyy????.????1?????? ???????
``???&??yyyy?????Ayyy·yyy ???? ???&?
?MathType??`????u1/4y ????

I?e oeueiio, yeui aea?aoe /anoioo ciai?oiuei? neee wmetafile8?
??????????????? ???????????yyy????.????1??????
??????? A????&??yyyy?????Ayyy*yyyA??—?? ???&? ?MathType??
????u@th??????

?en. 6. Caeaaei?noue ii?iiaaii? iioeaee a?aeiiaeaiiai neaiaeo a?ae
ii?iiaaii? ?ioaineaiino? ooio a eaiae? ca’yceo i?e ??ci?e oe?ei? nioae
o?eueo?o ieae/eo /anoio ia aeoiae? i?eeia/a.

AENIIAEE

Iniiai? ?acoeueoaoe, iaea?aeai? a aeena?oaoe??, oa aeniiaee, ui
noi?ioeueiaaii, caiaeyoueny aei ianooiiiai.

1. ?ic?iaeaii iaoiaeeeo ioe?iee nenoaiaoe/ieo oa aeiaaeeiaeo iioeaie i?e
i?iaaaeaii? ?ic?aooie?a ei?aeyoe?eii? ?ici??iino? ca aeaieie
niinoa?aaeaiue.

2. Aaeineiiaeaii iaoaiaoe/i? ae?ace aeey aeai?o iniiaieo iioeiaeueieo
ia?aiao??a i?ioeaaeo?e ?ic?aooie?a ei?aeyoe?eii? ?ici??iino?, oaeeo ye
iaae? neaee?iaiaiai ?ioa?aaeo, e?euee?noue oi/ie, o?eaae?noue
?aae?caoe?? oa ?o ca’ycie c a?aeiioaiiyi neaiae/ooi.

3. C?iaeaii e?euee?ni? ioe?iee aieeao nioaiai? o?eueo?aoe?? ia ioe?ieo
ei?aeyoe?eii? ?ici??iino?. Aeine?aeaeaii aee?eaeaiiy, yeeo caaaeathoue
neaiaeo nioaia? ?aeaaeueiee o?eueo? oa oeeo?iaee o?eueo? ae?oaiai
ii?yaeeo.

4. Iaa?oioiaaii iiaeeea?noue ?ic?aooieo ei?aeyoe?eii? ?ici??iino?
neaiae?a, ye? caciaee aieeao nioaiai? o?eueo?aoe??.

5. Cai?iiiiiaaio o aeena?oaoe?? iaoiaeeeo ai?iaiaaii ia
aenia?eiaioaeueieo aeaieo.

6. Io?eiaii ?acoeueoaoe aiae?co ei?aeyoe?eii? ?ici??iino? aeaieo
niinoa?aaeaiue i?e?naeoiaeieo ioeuenaoe?e niiy/iiai
?aae?iaei?ii?ithaaiiy a ae?aiacii? /anoio 2.5 oa 2.85 AAoe oa aeiaaaeaii
a?aenooi?noue oaioe/ieo eieeaaiue o ?aae?caoe?yo, ye? aoei
aeine?aeaeaii.

7. Aeine?aeaeaii noaie aeei?enoaiiy oaioe/ieo eieeaaiue a caaea/ao
eiaeoaaiiy oa aeaeiaeoaaiiy ?ioi?iaoe??, ye? ia aeei?enoiaothoue yaeua
oaioe/ii? neio?ii?caoe??.

8. Cai?iiiiiaaii caniae iicaaaeaiiy a?ae ooi?a o oeeo noaiao oa
i?iaaaeaii aiae?c yeino? ianeoaaiiy oa a?aeiiaeaiiy neaiaeo, ui
ia?aaea?oueny.

Ioae?eaoe?? aaoi?a ca oaiith aeena?oaoe??

[1] Aaa?ea Ae.I., Eeoaeiaiei E.I., ?yaia A.A., Noaiaiia A.A., Onee I.A.,
TH?ianeee TH.O. Aeeiaie/aneay no?oeoo?a iee?iaieiiaiai eceo/aiey
nieia/iie aniuoee // Aeieeaaeu Aeaaeaiee Iaoe Oe?aeiu.-1992.- ?7.-N.
75-78.

[2] Ryabov V. B., Stepanov A.V., Usik P.V., Vavriv D.M., Vinogradov
V.V., Yurovskiy Yu.F. From chaotic to 1/f processes in solar mcw-burst
// Astronomy and Astrophysics.-1997.-V.324.-P. 750-762.

[3] Ryabov V.B., Usik P.V., Vavriv D.M. Chaotic masking without
synchronization // ?aaeeioeceea e ?aaeeiano?iiiiey.-1997.-O.2, ?4-
N.473-479.

[4] Litvinenko L.N., Ryabov V.B., Usik P.V., Vavriv D.M. Correlation
Dimension: The New Tool in Astrophysics. –Oa?ueeia:1992.- 54n. (I?ai?eio
/ ?aaeeiano?iiiie/aneee Einoeooo AI ONN?, ?64).

[5] Aaa?ea Ae.I., ?yaia A.A., Onee I.A. Ei??aeyoeeiiiay ?acia?iinoue e
ia?aaioea eioi?iaoeee // Oacenu aeieeaaeia XVII Iaaeio?aneaaie
iao/ii-oaoie/aneie eiioa?aioeee “Iaoiaeu e ono?ienoaa ia?aaioee
?aaeeieieaoeeiiiie e ?aaeeioaoie/aneie
eioi?iaoeee”.-Eeaa.-1992.-N.26-28.

[6] Ryabov V.B., Usik P.V., Vavriv D.M. Chaotic encoding of information
without synchronization // Proc. of Intern. Conf. on «Applied nonlinear
dynamics and stochastic systems near the millenium” (AIP Conf.
Proc.411).- San Diego (CA,USA).- 1997.- P.329-333.

Aiioaoe??.

On?e I.A. ?ic?iaea oa ai?iaaaeaeaiiy o?aeoaeueieo iaoiae?a aiae?co
oaioe/ieo nenoai.-?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe c niaoe?aeueiino? 01.04.03 – ?aae?io?ceea.
?inoeooo ?aae?io?ceee oa aeaeo?ii?ee ?i. I. ss. On?eiaa IAI Oe?a?ie,
Oa?e?a, 1999.

A ?iaio? cai?iiiiiaaii iaoiaeeeo ioe?iee nenoaiaoe/ieo oa aeiaaeeiaeo
iioeaie i?e i?iaaaeaii? ?ic?aooie?a ei?aeyoe?eii? ?ici??iino?,
aaeineiiaeaii e?eoa??? aeai?o iioeiaeueieo ia?aiao??a oaei? i?ioeaaeo?e.
Iaaaaeaii ioe?iee aieeao nioaiai? oeeueo?aoe?? ia ei?aeyoe?eio
?ici??i?noue oa aee?eaeaiue, yeeo caaaeathoue neaiaeai o?eueo?e ae?oaiai
ii?yaeeo oa ?aeaaeuei?. Iaoiaeeeo ai?iaiaaii ia aenia?eiaioaeueieo
aeaieo. I?iaiae?ciaaii i?e?naeoiaei? ioeuenaoe?? ?aae?iaei?ii?ithaaiiy
Niioey a ae?aiacii? /anoio 2.5 oa 2.85 AAoe. Aeine?aeaeaii i?aeo?ae aei
aeei?enoaiiy aeaoa?i?iiaaiiai oaino o caaea/ao eiaeoaaiiy oa
aeaeiaeoaaiiy ?ioi?iaoe??, yeee ia aaco?oueny ia yaeu? oaioe/ii?
neio?ii?caoe??. Cai?iiiiiaaii caniae iicaaaeaiiy a?ae ooi?a oa io?eiaii
e?euee?ni? ioe?iee aieeao ?o ia?aiao??a ia ye?noue ianeoaaiiy ?
a?aeiiaeaiiy neaiaeo, ui ia?aaea?oueny.

Eeth/ia? neiaa: oaioe/i? nenoaie, o?aeoaeueiee aiae?c, ei?aeyoe?eia
?ici??i?noue, o?eueo?aoe?y, ia?iaea, eiaeoaaiiy oa a?aeiiaeaiiy
?ioi?iaoe??.

Onee I.A. ?ac?aaioea e aiaae?aiea o?aeoaeueiuo iaoiaeia aiaeeca
oaioe/aneeo nenoai. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.03. – ?aaeeioeceea.
Einoeooo ?aaeeioeceee e yeaeo?iieee ei. I. ss. Oneeiaa IAI Oe?aeiu,
Oa?ueeia, 1999.

Aeenna?oaoeeiiiay ?aaioa ninoieo ec aaaaeaiey, /aou?ao aeaa e auaiaeia.
Nienie eniieueciaaiuo enoi/ieeia niaea?aeeo 105 iaeiaiiaaiee. Ia?aay
aeaaa niaea?aeeo iaci? eeoa?aoo?u ii oaia ?aaiou.

Ai aoi?ie aeaaa aeenna?oaoeeiiiie ?aaiou ?ac?aaioaia nia?aiaiiay
iaoiaeeea ioeaiee nenoaiaoe/aneeo e neo/aeiuo iia?aoiinoae, aicieeathueo
i?e ?an/aoa ei??aeyoeeiiiie ?acia?iinoe ii iaaethaeaoaeueiui aeaiiui.
?anniio?aia iauay noaia oaeeo ?an/aoia. Auaeaeaiu iniiaiua enoi/ieee
ioeaie ii?aaeaeaiey ei??aeyoeeiiiie ?acia?iinoe. Ia i?eia?ao iiaeaee,
eioi?ay iienuaaao aeeiaieeo ianneaiie iiaeu, aiaea/aiiie a oo?aoeaioiia
aeaeaeaiea, iieacaii aeeyiea auai?a a?aiaie caaea?aeee e ei??aeyoeee
aeeceeo ii a?aiaie oi/ae ia ioeaieo o?aeoaeueiie ?acia?iinoe.
Oai?aoe/anee iainiiaaiu e?eoa?ee auai?a iioeiaeueiuo ia?aiao?ia, oaeeo
eae a?aiy caaea?aeee, a?aieoeu neaeeeiaiaiai eioa?aaea, /enei oi/ae,
aeeeia ?aaeecaoeee, a oaeaea eo naycue n ioiioaieai neaiae/ooi. Iieo/aiu
caaeneiinoe eo aeeyiey ia ioeaee ?an/aoa ei??aeyoeeiiiie ?acia?iinoe.
Eceiaeaiu ?aeiiaiaeaoeee ii ieaie?iaaieth e i?iaaaeaieth yenia?eiaioia n
oeaeueth iieo/aiey aeaiiuo aeey enneaaeiaaiee iaoiaeaie oai?ee
aeeiaie/aneeo nenoai.

A o?aoueae aeaaa ?anniio?aia iaoaiaoe/aneay iiaeaeue i?ioiaeaeaiey
neaiaea /a?ac i?eaiii-ia?aaeathuea ono?ienoaa a aeaea iieiniauo
oeeueo?ia. I?e iiaeaee?iaaiee, a ea/anoaa oaioe/aneiai neaiaea,
iiaeaa?aathuaainy oeeueo?aoeee, eniieueciaaeny neaiae, iieo/aiiue ec
o?aaiaiey Iaeeay-Aeanna. Iainiiaai ?an/ao o?aeoaeueiie ?acia?iinoe ii
yenia?eiaioaeueiui aeaiiui, o eioi?uo, i?e i?ioiaeaeaiee /a?ac iieiniaua
oeeueo?u, ia?acaaony /anoue iieinu oa?aeoa?iuo /anoio enneaaeoaiiai
neaiaea. I?eaaaeaiu ioeaiee eneaaeaiee, i?eaiineiuo a ?an/aou
ei??aeyoeeiiiie ?acia?iinoe oeeueo?iaaiiiai neaiaea n ?acia?iinoueth
auoa o?ao iieiniauie oeeo?iauie eaeaaeueiui oeeueo?ii e oeeueo?ii
aoi?iai ii?yaeea. Enneaaeiaaiey i?iaaaeaiu eae ia oe?ieiiieiniuo, oae e
oceiiieiniuo neaiaeao. Iino?iaiu a?aoeee caaeneiinoae cia/aiey
ei??aeyoeeiiiie ?acia?iinoe aeey ?acee/iuo aaee/ei oe?eiu iieinu
i?iioneaiey e cia/aiee oeaio?aeueiie /anoiou iieiniauo oeeueo?ia aeey
iaieo oeiia oeeueo?ia.

Oaeaea a yoie aeaaa eceiaeaiu ?acoeueoaou i?eiaiaiey iaoiaeeee ?an/aoa
ei??aeyoeeiiiie ?acia?iinoe aeey aiaeeca aeaiiuo iaaethaeaiee
ieeeeiao?iauo ioeuenaoeee ?aaeeieceo/aiey Nieioea a aeeaiaciiao /anoio
2.5 e 2.85 AAoe. Iniiauaaynue ia aiaeeca ?an/aoia, i?iaaaeaiiuo aeey
caienae naie niauoee, naeaeaiu auaiaeu ia ionoonoaee a eceo/aiee
nieia/iuo aniuoae ia yoeo /anoioao oaioe/aneeo eiiiiiaio n iaeui
cia/aieai ?acia?iinoe. Iieo/aiua ?acoeueoaou niaiaaeatho n ?acoeueoaoaie
aiaeiae/iuo enneaaeiaaiee ia ae?oaeo /anoioao, i?iaiaeeiuo ca?oaaaeiuie
enneaaeiaaoaeyie.

*aoaa?oay aeaaa iinayuaia ?anniio?aieth iiaeoiaea e eniieueciaaieth
aeaoa?ieie?iaaiiiai oaina a caaea/ao eiaee?iaaiey-aeaeiaee?iaaiey
eioi?iaoeee, eioi?ue iniiaai ia eiaa?oe?iaaiee oaioe/aneeo aeeiaie/aneeo
nenoai. Enneaaeiaaiu noaiu ianee?iaee e ainnoaiiaeaiey eioi?iaoeeiiiuo
neaiaeia, aace?othueany ia aaoiiiiiie nenoaia ?annea?a e iaaaoiiiiiii
o?aaiaiee iayoieea e ia eniieuecothuea yaeaiea oaioe/aneie
neio?iiecaoeee. Eniieuecoy a ea/anoaa iieaciiai eioi?iaoeeiiiiai neaiaea
neionieaeo, neaiae n aunieei cia/aieai ?acia?iinoe, iieo/aiiue i?e
eioaa?e?iaaiee o?aaiaiey Iaeeay — Aeanna e ioeeo?iaaiiua caiene caoea,
iieo/aiu eiee/anoaaiiua ioeaiee aeeyiey ia?aiao?ia i?aaeeiaeaiiuo noai
ia ea/anoai ianee?iaee e ainnoaiiaeaiey ia?aaeaaaaiiai neaiaea.
I?aaeeiaeaiu niiniau iiaeaaeaiey aaeaeeoeaiuo ooiia a eaiaea nayce e
au/eneeoaeueiuo iia?aoiinoae aeeooa?aioee?iaaiey a oaeeo noaiao.
Ioeaiaii aeeyiea ?anno?ieee ia?aiao?ia oaioe/aneeo nenoai ia ioeaee
ainnoaiiaeaiey eioi?iaoeeiiiiai neaiaea. Iooai iino?iaiey aeeiaie/aneiai
niaeo?a enneaaeiaaii ea/anoai ianee?iaee. I?iaaaeaii n?aaiaiea
enneaaeoaiiai iiaeoiaea e iiaeoiaea, iniiaaiiai ia neio?iiecaoeee.
Iieo/aiu caaeneiinoe ioiioaiey neaiae/ooi ia aoiaea ia?aaeao/eea e
auoiaea i?eaiieea i?e eniieueciaaiee i?aaeeiaeaiiiai niiniaa iiaeaaeaiey
ooiia. ?anniio?aiu i?aeiouanoaa e iaaeinoaoee i?aaeeaaaaiie noaiu
ainnoaiiaeaiey iieaciie eioi?iaoeee.

Eeth/aaua neiaa: oaioe/aneea nenoaiu, o?aeoaeueiue aiaeec,
ei??aeyoeeiiiay ?acia?iinoue, oeeueo?aoeey, ia?aaioea, eiaee?iaaiea e
ainnoaiiaeaiea eioi?iaoeee.

Usik P.V. Development and introduction of the fractal methods of chaotic
systems analysis. – Manuscript.

A dissertation in partial fulfillment of the requirements for the
Candidate of Science degree in Physics and Mathematics (specialty code
01.04.03 – Radio Physics). Usikov’s Institute of Radiophysics and
Electronics NASU, Kharkov, 1999.

The paper presents the procedure systematic and random error
evaluations of correlation dimension calculation and the criterions for
optimal parameters choice are developed. The quantitative evaluation of
influence of band-pass filtration to nirrelation dimension and
evaluation of distortion for ideal and two-order filters are given. Ohe
procedure was used for experimental data processing. Sun radiation in
the range 2.5 and 2.85GHz are analyzed. The method for the deterministic
chaos usage for information coding and decoding without synchronization
is investigated. Methods of noise reduction are proposed; and
quantitative evaluation of parameters impact for signal quality masking
and restoring is obtained.

Key words: chaotic systems; fractal analysis, correlation dimension,
filtering, processing, coding and restoring of information

Iaoeiaa aeaeaiiy

On?e Iaaei A?eoi?iae/

?IC?IAEA OA AI?IAAAeAEAIIss O?AEOAEUeIEO IAOIAe?A AIAE?CO OAIOE*IEO
NENOAI

I?aei.aei ae?oeo 15.09.99. Oi?iao 60O84 1/16

Iai.ion. O?aoa?aoia. ia/.Oi.-ia/.a?e.1,25.

Oe?aae 100 i?ei.Cai. 16.Aac oe?ie.

Iaae?oeiaaii o ae?oea?i? OIA “Aoeaio-N”

310002, i.Oa?e?a, aoe. ?aaeia?eii?anueea,13

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