Background: Psychopathology research is changing focus from group-based ‘disease models’ to a personalized approach inspired by complex systems theories. This approach, which has already produced novel and valuable insights into the complex nature of psychopathology, often relies on repeated self-ratings of individual patients. So far it has been unknown whether such self-ratings, the presumed observables of the individual patient as a complex system, actually display complex dynamics. We examine this basic assumption of a complex systems approach to psychopathology by testing repeated self-ratings for three markers of complexity: memory, the presence of (time-varying) short- and long-range temporal correlations, regime shifts, transitions between different dynamic regimes, and, sensitive dependence on initial conditions, also known as the ‘butterfly effect’, the divergence of initially similar trajectories.Methods: We analysed repeated self-ratings (1476 time points) from a single patient for the three markers of complexity using Bartels rank test, (partial) autocorrelation functions, time-varying autoregression, a non-stationarity test, change point analysis and the Sugihara-May algorithm.Results: Self-ratings concerning psychological states (e.g., the item ‘I feel down’) exhibited all complexity markers: time-varying short- and long-term memory, multiple regime shifts and sensitive dependence on initial conditions. Unexpectedly, self-ratings concerning physical sensations (e.g., the item ‘I am hungry’) exhibited less complex dynamics and their behaviour was more similar to random variables. Conclusions: Psychological self-ratings display complex dynamics. The presence of complexity in repeated self-ratings means that we have to acknowledge that (1) repeated self-ratings yield a complex pattern of data and not a set of (nearly) independent data points, (2) humans are ‘moving targets’ whose self-ratings display non-stationary change processes including regime shifts, and (3) long-term prediction of individual trajectories may be fundamentally impossible. These findings point to a limitation of popular statistical time series models whose assumptions are violated by the presence of these complexity markers. We conclude that a complex systems approach to mental health should appreciate complexity as a fundamental aspect of psychopathology research by adopting the models and methods of complexity science. Promising first steps in this direction, such as research on real-time process-monitoring, short-term prediction, and just-in-time interventions, are discussed.
Complex dynamics and control investigation of a Cournot triopoly game formed based on a log-concave demand function
