Task 6 Flashcards
How did we used to describe natural systems ?
- In terms of linear equations
- X = Y
- Also called continous behavour change
By what and why did linear equations got replaced ?
- They can only describe smooth part but no jumping of behaviour could be explained
- Replaced by: Dynamic system
What is meant by a dynamic system ?
- It is a set of elements that interact and continaully evolve over time
- Either linear or non linear
- Example: The weahther system
What is meant by a linear equation ?
- Part of complex dynamic systems
- variable depend on interaction of values
- y=xz
- it often provides multiple solution
- Can explain complex systems
What is one unique characteristic of erratic behaviour ?
- Erratic behaviour
What does erratic behaviour mean ?
- tend to jump from one point in the space to another completely different one in a short period of time
What are three properties of complex dynamic systems ?
- State space
- Attractors
- Chaos
What is meant by state space ?
- Those are all possible states of a system
- states are determined by different variable combinations
- It can also capture changes in dynamic systems
What is meant by an attractor ?
- Visually they look like circles
- General defi: those are typical stable states where they system wants to settle into
- we have multiple attractors
- Dynamic system want to predict the attractors to know which behaviour is most likly to occur
What is meant by basin of attraction ?
- All the points within a state space that will move towards a attractor
What is meant by phase transition ?
- change from one attractor to another attractor
What is meant by chaos ?
- Basically that a dynamic system can be a chaotic sytsem
- chaotic system = very sensitive to intial condition
What is meant by “sensitve to initial condition” ?
- small differences in values of the variables lead to dramatically different outcomes as the system develops -> in the same equation
- In short: Two point start at allmost the exact same point but then end up in complete different points
What is meant by the butterfly effect ?
- small initial differences may lead to large unforeseen consequences over time
Can we based on a dynamic system forsee future bahviour ?
- Because complex dynamic system include chaos, it is only possible to predict general pattern of behaviour
- Conclusion we can not predict specific behaviiour which will occur in the long run
Why do people have stable but unpredictable patterns of behaviour?
- Attractors explain the stable patterns
- but since there are multiple attractors it occurs that there will be a transition from one to another during unstable phases (flactuations)
How do we call the predictable parts in a chaotic systems ?
- self organization ilands
- very robust
What is meant by self organization ?
- > self organization means sponatenous order
- it is a process where order arises from local interactions between parts of initally disorder systems
- SO is not caused by external factors it only needs a sufficient amount of energy
- often triggerd by fluctuations and positive feedback
- often occurs after reaching a certan
What is a general characteristics of self organizations ?
- it is a cyclical state change
What is meant by catastrophe theory ?
- it explains sudden shift in behaviour caused by small changes in circumstances,
- 3 types of catastrophe theory
- describe discontinuity in a single dependent (behavioural) vraiable
- all non linear
Name the 3 types of
- Fold catastrophe ( 1 independent V)
- cusp catastrophe (2 independent V)
- butterfly catastrophe (4 independent V)
Decribe the cusp theory a bit more in depth:
- it is a 3D model
- One part is the control surface which contain both independent variable ( love and social pressure ) -> Horizontal
- And then we have the behavioural dimension (vertical)
- Special about the model it contains a fold curve and the bifurcation set
What is meant by the fold curve ?
- the points who lie on the bifuracttion set will be presented in the fold curve
- The fold curve represents two possible behaviours (outcomes) of one equation = outcom of bimodality
- Also called the catastrophic jump
What is meant by the bifuraction set ?
- all the points that are presented in the fold curve
- a certain area
- Bimodality