Natural systems Flashcards
What is the formula for Euler’s method
What is the local error in Euler’s method
O(dt^2)
What is the global error in Euler’s Method
O(dt)
What are the conditions of stability in a equilibrium point
for step +dt
f’(x+dt) > 0: unstable
f’(x+dt) < 0: stable
f’(x+dt) = 0:
f’‘(x+dt) < 0: stable
f’‘(x+dt) > 0: unstable
What is the product rule
d/dt (uv) = u v’ + u’ v
What is the quotient rule
d/dt (u/v) = (v u’ - u v’)/v^2
What is an autonomous system
A system which does not explicitly contain t
What is a non-autonomous system
A system which explicitly contains t
what is the formula for the mid point method
What is the RK2 formula
What is the RK4 formula
What is the equilibrium condition for 2D ODEs
How do we study the stability of an equilibrium point in multiple dimensions
We compute the Jacobian at the equilibrium point and study the signs of the eigenvalues
What is the eigenvalue and eigenvector equation for the Jacobian
v is the eigenvectors, lambda is the eigenvalues
What are the stability conditions on eigenvalues
if both are negative then stable, If both are positive then unstable, if different signs, then it is a saddle point, which is unstable.
What is the idea behind agent based modelling
We encode realistic behaviours (both logical and random) into agents, these agents can then be allowed to interact within a realistic environment,
What are the two types of communication in agent based modelling
Direct communication
Indirect communication
what is direct communication in ABM
in an interaction between agents, their status is directly updated. This is easy to implement but interactions are harder to track. Synchronous updates are not possible.
What is indirect communication in ABM
When agents interact, they send a message which will be acted on later. Allows interactions to be tracked, harder to implement
What are the two types on indirect communication in ABM
Global message lists:
All agents write messages to a global list
Local message lists:
Agents write messages to a local table,
code can be parallelised.
What are the two types of updates in ABM
Asynchronous - messages are acted upon immediately, the agent acting first may have an advantage
Synchronous - messages are acted upon at the same time, order is not important, but may act on incorrect information
What is the heuristic for drawing 2D phase plots
If the system has opposite sign eigenvalues: Saddle point: follow eigenvector directions
If the system has the same sign eigenvalues:
consider the behaviour at different points. Lines will go to/ start from equilibrium.
Complex:
Real part +ve -> spiral away from eqm point
real part -ve -> spiral toward eqm point
What are the main parts of a neuron
Dendrites - Input device
Soma - CPU
Axon - Output
What is the formula for the leaky integrate and fire model