Dinamika enodimenzionalnih sistemov

Authors

Vladimir Grubelnik
University of Maribor, Faculty of Natural Sciences and Mathematics
https://orcid.org/0000-0002-4182-8520
Marko Marhl
University of Maribor, Faculty of Natural Sciences and Mathematics
https://orcid.org/0000-0003-0387-1162

Keywords:

system dynamics, feedback loops, stability analysis, bifurcations, logistic map, chaos

Synopsis

Dynamics of One-Dimensional Systems. The textbook addresses one-dimensional dynamic systems with an elementary approach. The goal is to enable students to better understand the fundamental principles of system dynamics, such as identifying stationary states, stability analysis, bifurcations, and the long-term behavior of systems. The textbook is primarily designed for physics students, but it is also useful for other disciplines where mathematical modeling of dynamic systems is part of the curriculum. The content sections of the textbook cover the basic characteristics of dynamic systems, the geometric approach to solving one-dimensional systems, flows on a circle, bifurcations and their characteristics, one-dimensional mappings (maps), and numerous examples of one-dimensional systems in physics, biology, and chemistry. The examples are selected to help students develop intuition for the dynamics of more complex multi-dimensional systems they encounter in everyday life.

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Author Biographies

Vladimir Grubelnik, University of Maribor, Faculty of Natural Sciences and Mathematics

Vladimir Grubelnik is an Associate Professor of Physics at the University of Maribor. He teaches at FERI and FNM. His research is focused on the mathematical modeling of dynamic systems, with an emphasis on biological cellular systems. The majority of his research focuses on the mathematical modeling of cellular processes from an energetic perspective. The significance of his research is reflected in the understanding of metabolic and signaling cellular pathways in relation to pancreatic alpha and beta cell pathology. Part of his research is also focused on the transfer of mathematical modeling to the field of education.

Maribor, Slovenia. E-mail: vlado.grubelnik@um.si

Marko Marhl, University of Maribor, Faculty of Natural Sciences and Mathematics

Marko Marhl is a Professor of Physics at the University of Maribor. He lectures at the Faculty of Education, Faculty of Medicine, and Faculty of Natural Sciences and Mathematics. His research focuses on system dynamics, primarily in biophysical systems. His specialty is mathematical modeling of signaling and metabolic processes at the level of biological cells. Most of his research is on the alpha and beta cells of the pancreas. The significance of his research is reflected in the understanding of the pathologies of these cells, which are mainly associated with metabolic syndrome and type 2 diabetes.

Maribor, Slovenia. E-mail: marko.marhl@um.si

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Published

February 13, 2024

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Details about this monograph

ISBN-13 (15)

978-961-286-826-0

COBISS.SI ID (00)

Date of first publication (11)

2024-02-13

How to Cite

Dinamika enodimenzionalnih sistemov. (2024). University of Maribor Press. https://doi.org/10.18690/um.fnm.1.2024