Reprezentace dynamických systémů s vnitřní síťovou strukturou
| Thesis title in Czech: | Reprezentace dynamických systémů s vnitřní síťovou strukturou |
|---|---|
| Thesis title in English: | Representation of dynamical systems with internal network structure |
| Key words: | komplexní sítě|náhodné sítě|synchronizace|dynamické systémy |
| English key words: | complex networks|random networks|synchronizations|dynamical systems |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Ing. et Ing. David Hartman, Ph.D. et Ph.D. |
| Author: | |
| Advisors: | Ing. Mgr. Jaroslav Hlinka, Ph.D. |
| Guidelines |
| Many dynamical systems, including natural ones such as brain or climate or protein interactions or technological ones such as the internet or WWW, are composed of smaller subsystems having their own dynamics. These subsystems are further interconnected by synchronization, forming thus the global dynamical behavior of the overall system. Such a system's overall behavior depends on the dynamics of particular subsystems and the character of interconnections. The interconnections structure has been shown to play a crucial role, also enabling representing the system with models mitigating the dynamics of the particular subsystems. Random graph models represent an extreme case of such simplification. This work aims to explore various types of random models with emphasis on their dynamical property, i.e., ability to evolve in time, modular character, i.e., ability to represent a characteristic hierarchy of the system, and global properties such as sparsity or controllability. |
| References |
| Porter, M. A., Gleeson, J. P. Dynamical systems on networks. in Frontiers in Applied Dynamical Systems: Reviews and Tutorials, Springer, 2016.
S. Boccaletti, A. Pisarchik, C. Genio, and A. Amann. Synchronization: From Coupled Systems to Complex Networks. Cambridge University Press, 2018. Newmann, M.E.J. Networks: an introduction. Oxford University Press, 2018. Barabasi, A.-L. Network Science. Cambridge University Press, 2016. Albert, R.; Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Modern Phys. 74(1):47-97, 2002. Frieze, A., Karonski, M. Introduction to random graphs, Cambridge University Press, 2016. Nešetřil, J. and Ossona de Mendez, P. Sparsity. Springer, 2012. van der Hofstad, R. Random graphs and complex networks. Cambridge University Press, 2016. |