Stabilnost diferencijalnih jednadžbi

Vopel, Ramona Mihaela (2016) Stabilnost diferencijalnih jednadžbi. Diploma thesis, Faculty of Science > Department of Mathematics.

[img]
Preview
PDF
Language: Croatian

Download (499kB) | Preview

Abstract

Differential equations have come to play an important role in many branches of science and industry. Stability theory addresses the following questions: Will a nearby orbit indefinitely stay close to a given orbit? Will it converge to the given orbit? We describe the ordinary differential equations, their classification, as well as the basic theorems of existence and uniqueness of solutions. A brief history of stability theory development is given, as well as stability definitions. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, above question may be reduced to a well-studied problem involving eigenvalues of matrices. In stability analysis of solutions of ODE, two methods are used: direct method and method of linearisation. Some techniques are shown to determine the Lyapunov function.

Item Type: Thesis (Diploma thesis)
Supervisor: Čaklović, Lavoslav
Date: 2016
Number of Pages: 37
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 22 Nov 2016 12:41
Last Modified: 22 Nov 2016 12:41
URI: http://digre.pmf.unizg.hr/id/eprint/5329

Actions (login required)

View Item View Item