Natural systems

Question 1

What is the formula for Euler’s method

Answer 1

Question 2

What is the local error in Euler’s method

Answer 2

O(dt^2)

Question 3

What is the global error in Euler’s Method

Answer 3

O(dt)

Question 4

What are the conditions of stability in a equilibrium point

Answer 4

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

Question 5

What is the product rule

Answer 5

d/dt (uv) = u v’ + u’ v

Question 6

What is the quotient rule

Answer 6

d/dt (u/v) = (v u’ - u v’)/v^2

Question 7

What is an autonomous system

Answer 7

A system which does not explicitly contain t

Question 8

What is a non-autonomous system

Answer 8

A system which explicitly contains t

Question 9

what is the formula for the mid point method

Answer 9

Question 10

What is the RK2 formula

Answer 10

Question 11

What is the RK4 formula

Answer 11

Question 12

What is the equilibrium condition for 2D ODEs

Answer 12

Question 13

How do we study the stability of an equilibrium point in multiple dimensions

Answer 13

We compute the Jacobian at the equilibrium point and study the signs of the eigenvalues

Question 14

What is the eigenvalue and eigenvector equation for the Jacobian

Answer 14

v is the eigenvectors, lambda is the eigenvalues

Question 15

What are the stability conditions on eigenvalues

Answer 15

if both are negative then stable, If both are positive then unstable, if different signs, then it is a saddle point, which is unstable.

Question 16

What is the idea behind agent based modelling

Answer 16

We encode realistic behaviours (both logical and random) into agents, these agents can then be allowed to interact within a realistic environment,

Question 17

What are the two types of communication in agent based modelling

Answer 17

Direct communication
Indirect communication

Question 18

what is direct communication in ABM

Answer 18

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.

Question 19

What is indirect communication in ABM

Answer 19

When agents interact, they send a message which will be acted on later. Allows interactions to be tracked, harder to implement

Question 20

What are the two types on indirect communication in ABM

Answer 20

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.

Question 21

What are the two types of updates in ABM

Answer 21

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

Question 22

What is the heuristic for drawing 2D phase plots

Answer 22

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

Question 23

What are the main parts of a neuron

Answer 23

Dendrites - Input device
Soma - CPU
Axon - Output

Question 24

What is the formula for the leaky integrate and fire model

Answer 24