#### Title

Information transfer in dynamical systems

Dissertation

2018

#### Degree Name

Doctor of Philosophy

#### Department

Electrical and Computer Engineering

#### Major

Electrical Engineering

Umesh Vaidya

#### Abstract

Causality analysis has been a topic of research from the days of Aristotle. However, there has not been an universal definition of causality, with different researchers providing different definitions and measures of causality. In this work, we provide a new definition of causality in a dynamical system setting. In particular, we quantify how a state (or subspace) of a dynamical system influence any other state (or subspace). The quantification is in terms of what we call information transfer. Intuitively, information transfer quantifies how the entropy of a state (say $y$) changes due to evolution of any other state (say $x$) and this characterizes the causal structure and influence in a dynamical system. We show that the information transfer measure satisfies intuitions of causality and influence. In particular, we show our information transfer measure satisfy \emph{(a) zero influence, (b) transfer asymmetry} and \emph{(c) information conservation}. The one step information transfer is generalized to define $n$-step information transfer and this enables us to clearly distinguish between direct and indirect influence. With this, we show how in a dynamical system setting, when previous measures of causality fail to capture the true causal structure, our information transfer measure do capture the true causal structure in a dynamical system. Apart from identification of causal structure, we use the information transfer measure to characterize influence and demonstrate how this can be used to characterize stability in a power network. In particular, we show how to identify the states and generators which are responsible for instability of a power network. Moreover, we show how the connection between stability and information transfer can be used to predict phase transitions in complex systems. We also provide two algorithms to compute information transfer from time series data and show how this can be used for topology identification of linear networks and stability analysis of power networks. Finally, as a separate application, we characterize influence in a stock market and also show how the information transfer measure can be used to predict stock market crashes.

#### DOI

https://doi.org/10.31274/etd-180810-6098

Subhrajit Sinha

en

application/pdf

177 pages

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