Nonlinear Systems Flashcards
What is the definition of a system?
A set of parts that are interconnected in effecting some joint outcome
Examples: Farm. Bike
System’s constituents
A set of elements and relations
2 fundamental types of system
Linear and Nonlinear
Linear system
Adheres to superpostion principals
What are the 2 superposition principals, and what do they outline?
Homogeneity: The output to a linear system is always proportional to the input
Additivity: We can add the effects of 2 system together and the result is a simple combination
Linear systems are called so because the results plotted on a graph results in what?
A staright line
Linear models do not accounts for systems where _______ are the main definer. What is an example of this?
relations
2 medicines that interact with each other
Linear models do not account for _____, as it takes no external feedback on how the action effects the environment
scale
We are just beginning to approach ________ _______
Nonlinear systems
_______ _______ do not adhere to the superposition principals
Nonlinear systems
Why does the Additivity Principal break down in nonlinear systems? What are some examples?
How we put things together matters.
Putting 2 creatures together get different interactions
Why does the Homogeneity Principal break down in nonlinear systems? What are some examples?
Fails to account if the outcome of the current state on the system would affect future states. IE Fails to account for feedback loops
Linear systems implies the possibility of _________ progress
continuous
What are 2 types of relations that result in non-additive combinations?
Synergies and Interference
Synergies
A positive interaction between 2 elements. Multiplying rather than adding an elements potentials
To achieve synergy
each elemtn must be differentiated and synchronised. Components must become different in respects to with each other
Interference
A combined system that is less than the sum of it’s components
Interfernece occurs
when there is a decisive lack of difeerence. results in competiion and crowding out. Like rush hour
Destructive relations
have a lack of feedback, which means componets never sync up
linear systems are
independant from inputs and outputs/ time
Feedback loop
A channel or pathway formed by an aeffect returning to its cause, causing more of the effect
what are 2 types of feedback loops. Define them
Negative: represents a relationship of constraint and balance. If one var changes in one direction, the other changes in the other. ex prices of items
Positive: Increase in one value is associated with increase in another value
Equilibrium
A linear system tends towards equilibrium when there is a negative feedback loop
And additive, negative feedback loop system has a net result of
zero, which is the systems equilibrium or normal state
Exponentials
describes a system in which the output feeds back as input, increasing the amount that is increasing each time, like a snowball effect. The rate of growth itself is growing in nonlinear systems
Power laws
Describes functional relationship between 2 quantitiesm, wehre one varies as a power of the other
Example is a cube volume
Metcalfe’s Law/networks effect -> key driver of positive feedback
Everytime we add a new computer to a network, we can add links as many as computers there are.
