What are complex systems?
Open systems consisting of many sub-systems that interact nonlinearly, showing emergent behavior
3 examples of emergent behavior
chaos, catastrophes and self-organization
What is the difference between weak and strong emergence?
Weak emergence = emergent phenomena mainly have descriptive value
Strong emergence = emergent phenomena have an independent causal role. Strong emergence is often associated with downward causation
What are the steps of the theory-construction methodology (TCM)?
- Identify the empirical phenomena that become the target of explanation.
- Formulate a set of theoretical principles that putatively explain these phenomena.
- Use this set or prototheory to construct a formal model, a set of model equations that encode the explanatory principles.
- Analyze the explanatory adequacy of the model, i.e., whether it actually reproduces the phenomena identified in step 1.
- Determine whether the explanatory principles are sufficiently parsimonious and substantively plausible.
What is the difference between data and phenomena?
Data are particular empirical patterns (a concrete dataset), whereas phenomena are general empirical patterns, stable and general features of the world
Three key observations about complex systems for use in psychology:
- Simplification: They can be simplified (e.g, traffic jam can be modeled without modeling lower-level systems like the cars themselves or the brains of the humans driving them)
- Equilibria: complex systems tend to be characterized by a limited number of equilibria (e.g Water normally exists in either a solid, liquid, or gaseous state: These are stable states over wide ranges of temperature and pressure. Also applies to psychology, e.g bipolar disorder, sleep stages, radicalization)
- Networks: complex systems are networks, as they consist of interacting subelements.
What are the two groups of models and methods for studying complex systems according to Sayama (2015)? (and which models belong to which group?)
(1) nonlinear dynamical system theory: for systems with a small number of variables.
Encompasses:
chaos theory
catastrophe or bifurcation theory.
(2) those for systems with many variables.
includes tools for studying multi-element systems eg:
agent-based modeling
network theory.
Why may long-term prediction be impossible even in the best of circumstances, where we have very accurate models and data?
Deterministic chaos
What equations are used for discrete or continuous time steps, respectively?
Continuous = Difference equations
Continuous = Differential equations
When is the fixed point (x*) found? (mathematically)
When X^(t+1) = X(t) = X*
What are the two types of fixed point attractors and what is the difference between them?
Unstable fixed point & stable fixed point. Stable = attracts from a wide range of initial values, unstable = easily perturbed (small change will cause X to move to a stable fixed point).
How can you determine (mathematically) whether a fixed point is stable or unstable?
Look at the derivative of the function f’(x). If the absolute value of the derivative in the fixed-point value is 1<, the fixed point is stable (otherwise unstable)
What is a limit cycle and what is the difference between (e.g) a limit cycle of period 2 and a limit cycle of period 4?
X oscillates between points. Period 2 = 2 points, Period 4 = 4 points
How do we plot phase plots for 1-dimensional systems?
x(t) against x(t+1).
How can we distinguish chaos from noise?
phase plots
What is a Burification graph?
Plots the equilibria as y-values for a range of r-values on the x-axis
A bifurcation graph is a diagram that shows how the qualitative behavior of a system changes, for example, from stable to chaotic, when one of its parameters changes.
