P - საქართველოს ტექნიკური უნივერსიტეტი

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P - საქართველოს ტექნიკური უნივერსიტეტი

zemoT aRwerili bifurkaciebi yvelaze ufro gavrcelebuliasxvadasxva bunebis mqone arawrfiv mravalganzomilebian dinamikursistemebSi. rasakvirvelia es bifurkaciebi ar moicaven ase-Ti tipis arawrfivi movlenebis mravalsaxovnebebs.bifurkaciuli diagramebi asaxaven arawrfivi dinamikuri sistemebisstatikur mdgomareobebs bifurkaciuli (mmarTveli) parametrebiscvlilebisas. sainteresoa sistemebis bifurkaciul mdgomareobazegadasvlis procesebis Seswavla drosa da sivrceSi.amasTan dakavSirebiT ganvixiloT dinamikuri procesebis iseTiarawrfivi sistemebis magaliTebi, romelTa evoluciuri gantolebebia“Cangali” da “andropov-hopfis bifurkacia’’[15].,,Canglis” tipis bifurkacia. maTematikuri TvalsazrisiTDdaqvemdebarebisprincipi sinergetikaSi eyrdnoba adiabaturimiaxlovebis meTods. an sxva sityvebiT, sawyisi sistemebis dayofisideaze nel da swraf qvesistemebad. amasTan erTad, xorcieldebacvladebis adiabaturi gamoricxvis procedura. daqvemdebarebisprincipis garda, sinergetikisaTvis Zalze mniSvnelovania,agreTve, wesrigis parametris cneba. am cnebebis arsi ganvixiloTmeore rigis arawrfivi sistemebis konkretul magaliTze, romelicaRiwereba Semdegi saxis gantolebiT [10]:& ( t)= λ Χ − ΧΥΧ1Υ&( t)= −λΥ + Χ22(1.21)sadac λ ≥ 10 ; λ2>0. aseTi diferencialuri gantolebebiT aRiwerebarigi procesebi fizikaSi, qimiaSi, ekologiaSi da a.S. vivaraudoTrom koeficienti λ 1Zalian mcirea da λ 2>> λ 1. Tu cvladebi Χda Υ mcireebia, maSin SeiZleba kvadratuli forma ΧΥ ugulebelvyoT,maSin Χ cvladi Seicvleba Zalze nela. Mmeore gantolebidanCans, rom nazrdi Υ ganisazRvreba wevriT da radganaccvladi Χ icvleba Zalian nela, unda velodoT, romΥ -icSeiZleba sakmaod nela Seicvalos. radganac λ 2>0 da bevrad metiaλ 1-ze, amitom warmoebuliΥ & (t)SeiZleba ugulebelvyoTλ 2Υ37

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