Bozorova dilfuza shavkat qizi

Obtained results and their novelty: in the Master's dissertation work. Based on foreign scientific literature and scientific articles, some models of dynamic systems and quadratic stochastic operators were analyzed.
Practical significance: The materials covered in this dissertation are of practical importance in explaining some models in biology, statistical mechanics, and in studying special courses on the theory of quadratic stochastic operators.
Level of implementation and economic efficiency: Today, the study of the evolution process through mathematical models is gaining importance. The results obtained by the theory of quadratic operators play an important role in this.
Field of application: The information presented on the topic studied in this dissertation can be used in the fields of biology, medicine, ecology, mechanics, probability theory and geology.

MUNDARIJA:

KIRISH…………………………………………………………………………..3
I BOB. CHIZIQLI OPERATORLAR HAQIDA TUSHUNCHA VA UNING TURLARI………………………………………………………………………..9
1. 1. Chiziqli operatorlar haqida tushuncha……………………………………..9
1. 2. Chiziqli operatorlarning turlari va ular ustida amallar……………………18
I bob bo‘yicha xulosa…………………………………………………………..32
II BOB. KVADRATIK STOXASTIK OPERATORLAR …….………………33

2.1. Kvadratik stoxastik operatorlar …………………..……………………….33

2.2. Kvadratik stoxastik operatorlarning qo`zg`almas nuqtalari………..……..40

II bob bo‘yicha xulosa….……………………………………………..……….45
III BOB. KVADRATIK STOXASTIK OPERATORLARGA OLIB KELINADIGAN BA’ZI MODELLAR ……………………………...……….46
3.1. Populyatsiyaning evolyutsion operatorini kvadratik stoxastik operatorga olib kelish………………………………………………………………………46
3.2. Statistik mexanikadagi Boltsman modelini kvadratik stoxastik operatorlar orqali ta`riflash.……………………………………………………………..…50
3.3. Biologiya va tibbiyotdagi ba’zi matematik modellar haqida…………..…52
III bob bo‘yicha xulosa………………………………………………….…….59
XULOSA VA TAKLIFLAR…………………………………………….……..60
FOYDALANILGAN ADABIYOTLAR RO’YXATI………………...……….62
ILOVALAR…………………………………………………………………
MUNDARIJA:

KIRISH……………………………………………………………………..	3
I BOB. CHIZIQLI OPERATORLAR HAQIDA TUSHUNCHA VA UNING TURLARI…………………………………………………………	9
1. 1. Chiziqli operatorlar haqida tushuncha………………………………...	9
1. 2. Chiziqli operatorlarning turlari va ular ustida amallar……………..	18
I bob bo‘yicha xulosa………………………………………………………	32
II BOB. KVADRATIK STOXASTIK OPERATORLAR…………………	33
2.1. Kvadratik stoxastik operatorlar ………………………………………	33
2.2. Kvadratik stoxastik operatorlarning qo`zg`almas nuqtalari………...	40
II bob bo‘yicha xulosa……………………………………………………	45
III BOB. KVADRATIK STOXASTIK OPERATORLARGA OLIB KELINADIGAN BA’ZI MODELLAR…………………………………...	46
3.1. Populyatsiyaning evolyutsion operatorini kvadratik stoxastik operatorga olib kelish………………………………………………………	46
3.2. Statistik mexanikadagi Boltsman modelini kvadratik stoxastik operatorlar orqali ta`riflash......................................................................	50
3.3. Biologiya va tibbiyotdagi ba’zi matematik modellar haqida………..	52
III bob bo‘yicha xulosa…………………………………………………….	59
XULOSA VA TAKLIFLAR……………………………………………….	60
FOYDALANILGAN ADABIYOTLAR RO’YXATI……………………..	62
ILOVALAR………………………………………………………………...	66

MUNDARIJA:

KIRISH……………………………………………………………………..	3
I BOB. Xususiy hosilali differensial tenglamalari haqida umumiy tushunchalar ………………………………………………………………..	9
1. 1. Xususiy hosilali differensial tenglamalari va ularning tarixi ………..	9
1. 2. Xususiy hosilali differensial tenglamalarning tasnifi ………………..	15
I bob bo‘yicha xulosalar……………………………………………………	25
II BOB. Elliptik tipdagi tenglamalar va ular uchun chegaraviy masalalar haqida ……………………………………………………………………..	26
2.1. Elliptik tenglama uchun chegaraviy masala haqida ………………….	26
2.2. Elliptik tenglamalari uchun chegaraviy masalalarning Grin funksiyalari haqida ………..........................................................................	36
2.3. Elliptik tenglama uchun masalasi Grin funksiyasining bahosi haqida………...............................................................................................	41
II bob bo‘yicha xulosalar…………………………………………………...	48
III BOB. Ikkita buzilish chizig’iga ega kvachiziqli elliptik tipidagi tenglama uchun Dirixle-Neyman masalasi……………………………….	49
3.1. Elliptik tenglama uchun Dirixle-Neyman chegaraviy masalasini yechimining yagonaligi haqida……………………………………………	49
3.2. Buzilish chizig'iga ega elliptik tipidagi tenglama uchun Dirixle-Neyman chegaraviy masalasining yechimini mavjudligi haqida.................	54
III bob bo‘yicha xulosalar………………………………………………….	62
XULOSA VA TAKLIFLAR……………………………………………….	63
FOYDALANILGAN ADABIYOTLAR RO’YXATI……………………..	65
ILOVALAR………………………………………………………………...	69