Global dynamics of some discrete dynamical systems with applications
Başlık çevirisi mevcut değil.
- Tez No: 403445
- Danışmanlar: Belirtilmemiş.
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2016
- Dil: İngilizce
- Üniversite: University of Rhode Island
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 148
Özet
Özet yok.
Özet (Çeviri)
In my rst manuscript, I investigate the global character of the di erence equation of the form xn+1 = f(xn; xn1); n = 0; 1; : : : (1) with several period-two solutions, where f is increasing in all its variables. I show that the boundaries of the basins of attractions of di erent locally asymptotically stable equilibrium solutions or period-two solutions are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium solutions or periodtwo solutions. An application of my results give global dynamics of three feasible models in population dynamics which includes the nonlinearity of Beverton-Holt and sigmoid Beverton-Holt types. In this paper I consider Eq.(1) which has three equilibrium points and up to three minimal period-two solutions which are in North-East ordering. More precisely, I will give sucient conditions for the precise description of the basins of attraction of di erent equilibrium points and period-two solutions. The results can be immediately extended to the case of any number of the equilibrium points and the period-two solutions by replicating my main results.In my second manuscript, I investigate the asymptotic behavior of the solutions of the system of di erence equation ~xn+1 = f(n; ~xn; :::; ~xnk); n = 0; 1; : : : ; where k 2 f0; 1; : : :g and the initial conditions are real vectors. I give some e ective conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation. My results are based on application of the linearization technique. I illustrate my results with many examples that include some transition functions from mathematical biology such as linear (also known as Holling type I functions) [5], Beverton-Holt (also known as Holling type II functions or Holling hyperbolic functions), sigmoid Beverton-Holt (also known as Holling type III functions or sigmoid functions) and exponential functions. In this paper I extend some of the results from [4] to the case of vector equation (21). In my third manuscript, I consider the cooperative system xn+1 = axn + by2n 1 + y2n yn+1 = cx2 n 1 + x2 n + dyn; n = 0; 1; : : : ; where all parameters a; b; c; d are positive numbers and the initial conditions x0; y0 are nonnegative numbers. I describe the global dynamics of this system in number of cases. An interesting feature of this system is that exhibits a coexistence of locally stable equilibrium and locally stable periodic solution as well as the Allee's e ect. All global dynamic results for this system can be extended to the general cooperative discrete system in the plane. In my fourth manuscript, I present some basic discrete models in populations dynamics of single species with several age classes. Starting with the basic Beverton-Holt model that describes the change of single species I discuss its basic properties such as a convergence of all solutions to the equilibrium, oscillation of solutions about the equilibrium solutions, Allee's e ect, etc. I consider the e ect of the constant and periodic immigration and emigration on the global properties of Beverton-Holt model. I also consider the e ect of the periodic environment on the global properties of Beverton-Holt model. In this paper I extend Theorems 34 -39 to the case of several generation model with special emphasis on three generation model. I prove general results about asymptotic stability. both local and global which cover all kind of transition or response functions such as linear , Beverton-Holt, sigmoid Beverton-Holt and exponential functions. In order to do so, I introduce some tools in Section 2 which contains some global attractivity results for monotone systems and some di erence inequalities results which lead to precise global attractivity results for non-autonomous asymptotically autonomous di erence equations. In Sections 3 and 4 I obtain fairly general results for local and global asymptotic stability of k-th generations model that extend all results in this section. In the special case of three generation model I nd the precise basins of attraction of all locally stable equilibrium solutions and locally stable period-two solutions.
Benzer Tezler
- Takviyeli dairesel silindirik kabuk yapıların serbest titreşimlerinin incelenmesi
Free vibrations of stiffened circular cylindrical shells
ZAHİT MECİTOĞLU
- Hibrit elektrikli araçlarda batarya performans ve yakıt tüketimi değerlerinin modellenmesi ve optimizasyonu
Modeling and optimization of battery performance and fuel consumption in hybrid electric vehicles
YAVUZ ERAY ALTUN
Doktora
Türkçe
2024
Makine Mühendisliğiİstanbul Teknik ÜniversitesiMakine Mühendisliği Ana Bilim Dalı
DOÇ. DR. OSMAN AKIN KUTLAR
- Numerical model of flue gas desulfurization spray tower in power plant
Enerji santrallerinde baca gazı kükürt arıtma sistemlerinin nümerik modeli
OSMAN GÖZÜTOK
Yüksek Lisans
İngilizce
2018
Kimyaİstanbul Teknik ÜniversitesiUçak ve Uzay Mühendisliği Ana Bilim Dalı
DR. BAYRAM ÇELİK
- Doğrusal olmayan sistemler için model öngörülü kontrol yöntemine ters optimal kontrol yapısının katılması
Injection of inverse optimal control structure to model predictive control method for non-linear systems
LÜTFİ ULUSOY
Doktora
Türkçe
2021
Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrolİstanbul Teknik ÜniversitesiKontrol ve Otomasyon Mühendisliği Ana Bilim Dalı
PROF. DR. MÜJDE GÜZELKAYA
- Hibrid elektrikli araçlar için enerji yönetim sistemleri
Energy management system for hybrid electric vehicles
EMRE KURAL
Doktora
Türkçe
2015
Makine Mühendisliğiİstanbul Teknik ÜniversitesiMakine Mühendisliği Ana Bilim Dalı
PROF. DR. BİLİN AKSUN GÜVENÇ