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Effects of Higher Order Interactions and Data-Driven Stability Analysis in Tipping Networks

Nikpanjeh, Fatemeh | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57655 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Rahimi Tabar
  7. Abstract:
  8. Recent studies in various fields such as the environment, climate, economics, and neuroscience have shown that many systems exhibit dynamic responses based on catastrophic shifts—sudden and unexpected changes in the system's state and behavior in response to environmental changes. One of the simplest cases of these shifts occurs when the dynamical bifurcation diagram of a system has a tipping point, which serves as a critical threshold for system parameters, allowing small disturbances to lead to significant changes in the system's state. Research on many natural systems has revealed that tipping elements as the subsystems of a complex system are not independent, and the tipping of one subsystem can trigger cascading tipping events in other subsystems, ultimately creating tipping cascades. In studies on tipping network dynamics, interactions between network components are often considered pairwise interactions, despite the non-linear nature of natural systems. It is crucial to involve higher-order interactions in our studies. Additionally, early prediction of such transitions in natural systems is highly important. Data-driven methods used as initial warnings for tipping events typically rely on statistical approaches such as data correlation analysis or variance examination. Exploring data-driven dynamical stability in such systems can be valuable. In this thesis, besides investigating the effects of complex system topology on tipping cascade phenomena, we delve into the impacts of high-order interactions among subsystems on the occurrence of tipping cascades. Furthermore, by presenting a data-driven method for reconstructing dynamics from time series, we analyze stability in tipping systems, providing practical insights as an early warning for tipping events
  9. Keywords:
  10. Tipping Cascade ; Stability Analysis ; Complex System ; Higher-Order Interactions ; Data Driven Method

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