Second order systems

Question 1

What are the conditions? (3)

Answer 1

• interconnection of several sub-systems
• 2 sub-systems = cascaded to each other
• suggest = dynamics of level A affectes dynamics of level B

Question 2

Features of LRD: (2)

Answer 2

• cascaded sub-systems = shown by rate of level B = dependent on level A (+ vice versa)
• @ least 2 feedback loops on cascaded sub-systems

Question 3

What are the characteristics of secondary systems?

Answer 3

• system response to step input
  = underdamped
  = critically damped
  = overdamped
• may have oscillatory behaviour

Question 4

Two LRDs:

Answer 4

Question 5

Lotka-Volterra
3 types of models:

Answer 5

cooperative
competitive
predator-prey

Question 6

Predator-prey model
prey = ____
predator = _____
parasite-host r/ships

Answer 6

host
parasite

Question 7

What are the assumptions of the predator-prey models? (6)

Answer 7

• prey = limited food supply
• predator depends on single prey for food supply
• only threat to prey = due to predator
• predator species = totally dependent on prey species as food supply
• rate @ which predators encounter prey = jointly proportional to sizes of 2 populations
• interactions between prey + predator leads to = death of
  prey

Question 8

Prey dynamics:

Answer 8

Question 9

Predator dynamics:

Answer 9

Question 10

LRD for predator-prey model:

Answer 10

more prey = more interactions between predator + prey = increased predator growth
= increased prey death

Question 11

What are the features of this graph? (6)

Answer 11

• results = oscillating behaviour
• phase lag between prey + predator = predator lags
• @ beginning = lower predator than prey = prey thrives
• as predators increase = prey decreased due to max. interaction between 2
• prey decreases = becomes too low ≠ enough food for predator
• predators decreases = prey increase

Question 12

Example: Glucose-insulin homeostasis Lotka Volterra

LRD=

Answer 12

Question 13

What are the differences between predator-prey vs glucose-insulin? (2)

Answer 13

difference from predator-prey
- no glucose-intake feedback loop
- no insulin-production feedback loop
BUT IS STILL SOS

Question 14

What happens when you:
1. increase B
2. reduce B

Answer 14

• increasing B = turn patient into type 2 diabetic
  not enough insulin/ insulin resistant
• reducing B = turn patient into type 1 diabetic
  pancreas ≠ produce enough insulin