Playing HAVOK on the Chaos Caused by Internet Trolls.

Trump supporting Twitter posting activity from right-wing Russian trolls active during the 2016 United States presidential election was analyzed at multiple timescales using a recently developed procedure for separating linear and nonlinear components of time series. Trump supporting topics were extracted with DynEGA (Dynamic Exploratory Graph Analysis) and analyzed with Hankel Alternative View of Koopman (HAVOK) procedure. HAVOK is an exploratory and predictive technique that extracts a linear model for the time series and a corresponding nonlinear time series that is used as a forcing term for the linear model. Together, this forced linear model can produce surprisingly accurate reconstructions of nonlinear and chaotic dynamics. Using the R package havok, Russian troll data yielded well-fitting models at several timescales, not producing well-fitting models at others, suggesting that only a few timescales were important for representing the dynamics of the troll factory. We identified system features that were timescale-universal versus timescale-specific. Timescale-universal features included cycles inherent to troll factory governance, which identified their work-day and work-week organization, later confirmed from published insider interviews. Cycles were captured by eigen-vector basis components resembling Fourier modes, rather than Legendre polynomials typical for HAVOK. This may be interpreted as the troll factory having intrinsic dynamics that are highly coupled to nearly stationary cycles. Forcing terms were timescale-specific. They represented external events that precipitated major changes in the time series and aligned with major events during the political campaign. HAVOK models specified interactions between the discovered components allowing to reverse-engineer the operation of Russian troll factory. Steps and decision points in the HAVOK analysis are presented and the results are described in detail.