The Complex Systems Approach
Course Guide
The Complex Systems Approach
Learning outcomes
Level of participant
For whom are these courses designed?
Admission requirements
Literature
Pre-course literature:
Selected chapters from these books will be made available so you can make a personal copy:
Notes about this book and the assignments
Schedule
We used
R
!
I Introduction
1
A Quick Guide to Scientific Rigour
1.1
Rigorous Open Science
Strong Inference
1.2
Theoretical Tunnelvision
So? What’s wrong?
No such thing as theory-free ‘facts’
Study Materials
Phenomena, theories, facts and laws
2
Introduction to Complexity Methods
2.1
The Complex Systems Approach
2.2
Ergodicity and the Measurment Problem
2.3
Component- vs. Interaction-dominant Dynamics
2.4
A Behavioural Science of the Individual?
Study Materials and Resources
Graphical representation of complex system properties
The Complexity Explorer Glossary
TED talks
Systems Innovation videos
II Mathematics of Change
3
Introduction to the Mathematics of Change
3.1
It’s a line! It’s a plane!
3.2
No! … It’s a time series!
3.3
Implementing iterative functions
3.4
Numerical integration to simulate continuous time
Euler’s method and more…
Analytical solution
Numerical solution (discrete)
3.4.1
Euler vs. Runge-Kutta
3.5
Deterministic Chaos
3.6
Modeling interactions between processes and agents
3.6.1
The Competetive Lottka-Volterra Equations
3.6.2
Predator-Prey (and other) dynamics as Agent Based Models
3.6.3
The dynamic field model
Study Materials and Resources
3.6.4
Differential equations
III Basic (Nonlinear) Time Series Analysis
4
Basic Time Series Analysis
4.1
Always plot your data!
4.2
Correlation Functions
4.3
Autoregressive models
5
Basic Nonlinear Time Series Analysis
5.0.1
Intuitive notion of Fractal Dimension
5.0.2
Coloured noise
5.1
Relative Roughness
5.2
Entropy
Physical Information and Entropy
Entropy in time series
5.3
Other measures in
casnet
Study Materials and Resources
Notes on Entropy
IV Scaling Phenomena - Fluctuation Analyses
6
Fluctuation Analyses: Global Scaling
6.1
Power Spectral Density (PSD) slope
6.2
Standardised Dispersion Analysis (SDA)
6.3
Detrended Fluctuation Analysis (DFA)
6.4
Other varieties of fluctuation analysis
Study Materials and Resources
Systems Innovation
7
Fluctuation Analyses: Local Scaling
7.1
Multi-fractal geometry in time series
7.2
Multi-fractal DFA
7.3
The Wavelet Transform Modulus Maxima (WTMM)
7.4
Multi-fractal Spectrum Measures
V Recurrence Based Analyses
8
Recurrence Quantification Analysis
9
Unordered Categorical Data
9.1
Categorical Auto-RQA
9.1.1
Auto-RQA Measures
9.1.2
The theiler window
9.2
Categorical Cross-RQA
9.2.1
Anisotropic and asymmetric categorical RQA measures
9.2.2
Diagonal (Cross) Recurrence Profiles
9.2.3
Chromatic RQA measures
10
Continuous Data
10.1
Phase Space Reconstruction
10.1.1
Choosing an embedding lag
10.1.2
False Nearest Neighbor analysis
10.2
Continous RQA measures
10.3
Multidimensional RQA
10.4
Continuous Cross-RQA
10.4.1
Anisotropic and asymmetric continuous RQA measures
11
An R interface to Marwan’s commandline recurrence plots
12
Computational load: The Python solution [PyRQA]
Setup the environment
VI Multivariate Timeseries Analysis
13
Vector Auto Regression (VAR)
14
Dynamic Complexity
Study Materials and Resources
Systems Innovation
15
Graph Theory and Complex Network Analysis
15.1
Recurrence Networks
ESM data
Reconstructed State Space
TS 2
TS 3
15.2
Multiplex Recurrence Networks
15.3
Time-varying Multiplex Recurrence Networks
15.4
Networks based on Multidimensional RQA
15.4.1
Extracting Phases
15.5
Transition Networks
APPENDICES
A
Some Notes on Using
R
A.1
New to
R
?
A.2
Getting started with
R
tutorials
A.3
Not new to
R
?
A.4
Time series analyses in R
Installing casnet
B
Working with time series in R
B.1
Plotting a
ts
object as a time series
B.2
Plotting multiple time series in one figure
B.3
The return plot
B.4
Using
ggplot2
C
Dealing with Missing Data
Data with missing values
C.1
Univariate imputation
Linear interpolation
Kalman filter
C.2
Multiple imputation
Auto-select method
Classification & regression trees
C.3
Compare different imputation methods
Visual inspection
Effect on analysis results
References
D
List of terms
Adaptive Behaviour
Analytic solution
Attractor
Basin of attraction
Behaviour (of a dynamic system)
Bifurcation
Bifurcation diagram
Catastrophe flags
Catastrophe theory
Complex Network
Complex system
Complexity science
Component dominant dynamics
Control parameter
Critical fluctuations
Critical slowing down
Deterministic Chaos
Difference equation
Differential equation
Dimension
Dimensions of a system
Dynamic system
Early warning signals
Effective Complexity
Embedding Dimension
Emergence
Entropy
Epigenetic landscape (potential landscape)
Experienced event
flow ~
Fractal
Fractal Dimension
Graph theory
Hausdorff Dimension
Holism (epistemic)
Idiographic approach
Information (quantity)
Initial condition
Interaction dominant dynamics
Iteration
Iterative function
Iterative system
Largest Lyapunov exponent
Limit cycle
Limit points
Linear function of predictors
Linear function of time
map …
Nonlinear dynamics
Orbit (trajectory)
Order
Order Parameter
Period-doubling
Phase portrait
Phase space
Phase transition
Potential function
Power-law scaling
Recursive process
Relaxation time
Repellors
Return map
Saddle point
Scale free network
Self-affinity
Self-similarity
Sensitive dependence on initial conditions
Small world network
State
State space
State space (phase space)
Strange attractor
System
Time series
Trajectory (orbit)
Transient time (transient behaviour)
References
Published with bookdown
The Complex Systems Approach to Behavioural Science
Chapter 15
Graph Theory and Complex Network Analysis