Task 6- M&M Flashcards
What are dynamic systems?
system whose changes over time can be characterized by a set of equations that show how current values of variables depend mathematically on previous values of those variables
What is a state space of a system?
- set of states it can be in as determined by the variables that are used to measure it
- e.g. weather model that keeps track of temperature, humidity, and air pressure at five locations has a total of fifteen variables, so all the different combinations of values of these variables constitute the state space
What does it mean if a dynamic system displays chaos?
if it is very sensitive to initial conditions, that is, if very small differences in values of variables of its equations can produce dramatically different outcomes as the system develops
What is the butterfly effect?
butterfly effect: a butterfly flapping its wings in China may have a tiny effect on the atmospheric system there that eventually leads to a major weather change elsewhere
What is the ‘dynamic systems challenge’ to cognitive science?
consists of the claim that, rather than understanding human thinking in computational representational terms, we should think of the mind as a dynamic system
What are the two responses to the dynamic systems challenge?
- Defender of CRUM could argue that the dynamic systems approach is very limited in its application to human thinking -> replace it
- Expand and supplement CRUM
What are linear dynamic systems?
Linear -> two or more equations whose solutions can be combined to obtain another solution; work well in physics but cannot always describe what happens in natural systems
What is non-linearity? What are nonlinear complex dynamic systems?
complex dynamic systems need to be described by nonlinear equations such as y = xz, where the value of the variable y depends on interaction of values of x and z
Which kind of behaviour can nonlinear systems show?
can have very erratic behaviour e.g. jumping from one point in the state space to another, very different point in a short period of time
What does it mean that nonlinear equations are not additive?
- Answers often involves pattern of solutions
2. Results feed back in system itself
What usually happens to nonlinear systems over time?
Settling down (or convergence) -> results in 1 of 4 typical patterns
What are the typical patterns called which nonlinear systems settle down into?
Attractors
What is discontinuity a subcategory of?
Subcategory of nonlinear
What characterizes discontinuity?
Sudden shifts; sudden or catastrophic jumps in behaviour
What is discontinuity often preceded by?
by an increase in variability and destabilization/ loosing of old, previous pattern that can be followed by system reorganization
What is a cusp catastrophe?
- Which type of system?
- What does it describe?
o One type of a nonlinear dynamic system
o Models of sudden and discontinuous change
o One of seven elementary catastrophe models that are developed
Why was the cusp catastrophe model developed for?
to describe complex natural and social phenomena
Which two kinds of variables does the cusp catastrophe model have?
two control variables (asymmetry variable and bifurcation variable)
Explain the example of the interaction between physiological arousal and cognitive anxiety.
- cognitive performance better when stressed until a certain threshold is reached
- if threshold reached -> catastrophic downfall
- sudden behavioural change exhibited once predictor variables cross cusp threshold
What are 5 features of the cusp catastrophe model?
- Bimodality
- Inaccessibility
- Divergence -> not settling down
- Hysteresis
- Abrupt transitions
What are attractors?
- Patterns a nonlinear system tend to settle down into
- Relatively stable states
Does a system only have one attractor?
No, a system may have multiple attractors ( more than one stable state)
What is a phase transition?
change from one attractor state to another constitutes a phase transition e.g. when the weather moves from being cool and clear to being hot
What are the 4 types of attractors?
(A) Point Attractor, (B) Cyclical or Oscillating Attractor, (C) Quasi periodic Attractor, (D) Chaotic Attractor
What are characteristics of the ‘chaotic attractor’?
- pattern is bounded, but after some repetitions within the system, it becomes very irregular
- Irregularity -> unpredictable
- unpredictability associated with “sensitive dependence on initial conditions”
- general patterns of future behaviour may be predictable but specific behaviors over the long range will not
What is self-organization?
process by which a structure or pattern emerges in an open system without specifications from the outside environment
What is ‘entrainment’?
- change of pattern with new energy
- another behaviour will disappear
- ability of one unit
- temporal coordination of behaviour of 2 units (synchronizing)
What are developmental transitions characterized by?
Periods of increased variability precede a range of developmental transitions (motor, cognitive and linguistic development; emotional behaviour)
How is the process of recovery of substance use like?
process is discontinuous
How is the system like during periods of fluctuations?
system is destabilized but also open to new information and to the exploration of potentially more adaptive associations and configurations
What are discontinuous transitions in psychotherapy preceded by?
preceded by critical fluctuations and instabilities in the system’s behaviour
Asymmetry variable
normal factor -> smooth, continuos
Bifurcation variable
splitting factor -> leads to discontinous change
Repeller
- negative form of attractor
- opposite of a magnet
- > chaos
- > you cannot settle
- > you’d push away
Hysteresis
- collection of stickiness
- between two states
- transition; shortly before you transition to other state
Settle
- cusp point
- you cannot stay there
- most unstable position
