The exploration of complex systems is a fundamental pursuit in various scientific disciplines, includingphysics, biology, finance and engineering. The inherent complexity and dynamics within these systemspose significant challenges for traditional analytical methods. In recent years, the emergence of Topological Data Analysis (TDA) has provided a promising framework for uncovering hidden structures andpatterns in dynamic data sets. This thesis investigates the application of Topological Data Analysis to analyze system dynamics,aiming to enhance our understanding of their behavior. Through a detailed review of existing literature,we examine the theoretical foundations of TDA and its relevance to discrete and continuous processes.We discuss conceptual underpinnings of persistent homology, a key technique in TDA, and its potentialfor capturing essential features of system dynamics. By applying TDA to two distinct models, thestochastic ODE and the discrete logistic equation, we demonstrate its effectiveness in revealing underlyingstructures that traditional methods might overlook, thereby offering new insights into the analysis ofstochastic and discrete dynamical systems.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-100062 |
| Date | January 2024 |
| Creators | Gafur, Md Abdul |
| Publisher | Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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