Task 6 Flashcards
Dynamic systems
Study of the way in which systems change over time. It explores the effect of various forces on system behavior and the manner in which systems seek their optimal state
Types of systems
Linear- change is modeled by 2 or more equations whose solution is combined to obtain another solution
- additive (not for dynamic systems)
Non-linear- complex dynamic systems need to be described in non-linear equations
- often not a single solution but a pattern of solution
- Iteration- exploring non-linear behavior
Erratic behavior
jumping from one point in space to a completely different one in a short period of time
State space
A set of states a system can be in as determined by the variables used to measure it (change in system= change in space)
Example: weather model: temperature, humidity, air pressure = variables that make up the space
Attractors
Nonlinear systems tend to settle down over time: often in one of four typical patterns
- stable state
- a system can have multiple attractors
Types:
a) point attractor
b) cyclical oscillating attractor
c) quasi periodic attractor
d) chaotic attractor
Phase transition
when one attractor changes into another attractor
Critical fluctuations: an important predictor of transition. When challenges to the current state of the system are too great to assimilate, change often is characterized by disturbances and increased variability in the system before reorganization.
- Afterwards the system settles into a new dynamic state (attractor) and variability decreases
Chaotic systems
very sensitive to initial conditions (irregular & unpredictable)
- if 2 conditions differ by a small amount at the onset time, there will be a completely different state after some time
- general patterns of future behavior may be predictable, but specific behaviors over the long range won’t
Mind as a dynamic system
We can think of the mind as a dynamic system and should try to develop equations that describe how the mind changes over time
- provides new sets of ideas and deals better with time than CRUM
- provides possible ways of meeting word challenge (mind interacts with a changing world)
- useful for describing non-representational aspects of human behavior (moods, motor control…)
Self-organization
The process by which a structure emerges in an open system without specifications from outside environment
- too much energy - may become unstable which gives rise to a variety of patters
GENERAL CHARACTERISTICS:
- multiple stable states change from one to other if critical threshold is crossed
- cyclical state changes
- structural coupling of component processes
- temporal, spatial and behavioral organization
- localized instabilities that can lead one part of the system to organize itself differently from another part of the system
- entrainment: the ability of one unit to cause other units to oscillate at a harmonically related frequency
- behavior that can sometimes be modeled by a system of nonlinear equations
Beluzhow-Zhabotinsky reaction (BZR):
behavior of the system can be defined in terms of a cyclical or even chaotic attractor and can be modeled by a system of nonlinear equations.
It exists in 2 different states
a) red state
b) blue state
It will oscillate between these states every 30 secs when stirred (doesn’t evolve towards fixed state)
If its not stirred: instability is created which triggers the formation of spiral or circular waves that slowly propagate through the system (spatial self-organization)
Self-organization & memory
When a rat smells an odor it sets off a burst of electrical activity which is in a wave form
- frequency and amplitude vary in an unreliable manner
- odor in brain represented by a spatial map, that makes the different odors distinguishable
when a new odor is learned, patterns for each odor change –> neural representation isn’t fixed
- possible to model the behavior of the olfactory bulb by using non-linear equations
CONS: the model does not correspond well to the actual EEG patter
Self-organization & clinical psychology
Number of non-linear models for clinical psychology has increased
- nonlinear transitions in mental states: certain states are very unstable in infants (walking etc)
CONS of such models:
- not knowing the factors and separating signal from noise
- confusion of concept and techniques among different fields
- how to test nonlinear hypotheses: use hypothesis about pattern, not about correlation
Catastrophe theory
One application of the dynamic system theory (non-linear).
- allows modeling of large catastrophic changes that result from small changes in the continuous predictor variable
Types of catastrophe theories
a) fold catastrophe - 1 independent variable
b) butterfly catastrophe - 4 independent variables
c) cusp catastrophe - 3 variables
Cusp catastrophe
Includes 3 variables:
a) ASYMMETRY VARIABLE (X)/ NORMAL FACTOR: outcome changes monotonically related to that factor
b) BIFURCATION VARIABLE (Y)/ SPLITTING FACTOR: increases in Y produce divergent behavior. Smooth changes –> sudden jumps
c) OUTCOME VARIABLE (Z)
All of that is displayed on behavioral surfaces, which build the stable regions of the system in space.
- control surface = lower surface
- behavior surface = upper surface
BIFURCATION SET: cusp shaped area
- Bimodality: for some points on control surface there are 2 points on behavior surface
(some people engage in certain behaviors while others won’t)
- Edges: threshold for catastrophic jump
- Catastrophic jump: a small change in independent variable will pass threshold & result in a sudden large increment in behavior variable
HYSTERESIS: dependency of state of a system on its history: the same set of current circumstances can produce very different behaviors
BISTABILITY: Dynamics of system determine which of 2 stable surfaces above bifurcation set is the equilibrium surface at any given time (determined by initial condition)
