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Thesis topic proposal
 
Ferenc Hartung
Stability and Stabilization of Discrete and Continuous Dynamical Systems with Delays

THESIS TOPIC PROPOSAL

Institute: University of Pannonia
computer sciences
Doctoral School of Information Science and Technology

Thesis supervisor: Ferenc Hartung
Location of studies (in Hungarian): University of Pannonia, Faculty of Information Technology, Department of Mathematics
Abbreviation of location of studies: PE


Description of the research topic:

Delayed difference and differential equations are often used to model engineering and biological systems. An important question is the examination of the stability and stabilizability of equilibrium solutions. An interesting theoretical and practical task is to analyze the dependence of the properties of solutions on parameters. For models with time-independent coefficients, the determination of the stability region and bifurcation properties is theoretically clear, and there are also numerical methods that can be used. For delayed models, especially for time-dependent delays, similar well-developed methods are not known, theoretical studies require complicated techniques. The aim of this research topic is to investigate open problems that cannot be answered due to the deficiencies of the theory, or can only be handled with computational tools and simulation techniques. It is also a task to apply and compare mathematical program packages, and to develop new effective programs and numerical methods for delayed differential and differential equations. Developed algorithms should be used to solve specific problems, such can be applied for compartment systems, population models, and neural networks.

Preliminary results can be found in the following publications:
A large number of publications have been published in the international literature on this subject, especially in the last decades. Current results of the supervisors have been published in international journals. A large number of publications is published in engineering or applied mathematical journals.

Number of students who can be accepted: 1

Deadline for application: 2023-02-28

 
All rights reserved © 2007, Hungarian Doctoral Council. Doctoral Council registration number at commissioner for data protection: 02003/0001. Program version: 2.2358 ( 2017. X. 31. )