The Complex Systems Approach

Complexity research transcends the boundaries between the classical scientific disciplines and is a hot topic in physics, mathematics, biology, economy as well as psychology and the life sciences. This course will discuss techniques that allow for the study of human behaviour from the perspective of the Complexity Sciences, specifically, the study of complex physical systems that are alive and display complex adaptive behaviour such as learning, development and creativity. Contrary to what the term “complex” might suggest, complexity research is often about finding simple models/explanations that are able to describe a wide range of qualitatively different behavioural phenomena. “Complex” generally refers to the object of study: Complex systems are composed of many constituent parts that interact with one another across many different temporal and spatial scales to generate behaviour at the level of the system as a whole, in complex systems “everything is interacting with everything”.

The idea behind many methods for studying the dynamics of complex systems is to exploit the fact that “everything is interacting” and quantify the degree of periodicity, nonlinearity, context sensitivity or resistance to perturbation (resilience) of system behaviour. Applications in the behavioural sciences are very diverse and concern analyses of continuous time or trial series data such as response times, heart rate variability or EEG to assess proficiency of skills, or health and well-being. Complexity methods can also be used for the analysis of categorical data, such as behaviour observation of dyadic interactions (client-therapist, child-caregiver), daily experience sampling, social and symptom networks. The complex systems approach to behavioural science often overlaps with the idiographical approach of “the science of the individual”, that is, the goal is not to generalise properties or regularities to universal or statistical laws that hold at the level of infinitely large populations, but to apply general principles and universal laws that govern the adaptive behaviour of all complex systems to a specific case, in a specific context, at a specific moment in time.

The main focus of the course will be hands-on data-analysis. Practical sessions will follow after a lecture session in which a specific technique will be introduced.

We will cover the following topics:

• Theoretical background of phase transitions (self-organised criticality), synchronisation (coupling dynamics) and resilience (resistance to perturbation) in complex dynamical systems and networks.
  
• Simple models of linear and nonlinear dynamical behaviour (Linear & logistic growth, Predator-Prey dynamics, Deterministic chaos),
  
• Analysis of (multi-) scale dependence in time and trial series (Entropy, Relative roughness, Standardized Dispersion Analysis, (multi-fractal) Detrended Fluctuation Analysis).
  
• Quantification of temporal patterns in time and trial series including dyadic interactions (Phase Space Reconstruction, [Cross-] Recurrence Quantification Analysis).
  
• Dynamical network analyses for univariate (recurrence networks) and multivariate time series (multiplex recurrence networks).
  
• Using the method of surrogate data analysis (constrained realisations of time series data) to test hypotheses about the nature of the data generating process.