Final Study Guide

Question 1

Positive Feedback loop

Answer 1

both signs on diagram are +

Question 2

Negative Feedback Loop

Answer 2

signs are opposite on diagram

Question 3

Sigmoid Function

Answer 3

(X^n)/(1+x^N)

Question 4

decreasing sigmoid Function

Answer 4

(1)/(1+x^N)

Question 5

logistic growth equation

Answer 5

rn(1-(n/k))

Question 6

Linear Stability Analysis

positive tangent line slope

Answer 6

unstable

Question 7

Linear Stability Analysis

negative tangent line slope

Answer 7

stable

Question 8

______________________ is a region of the state space for which when you get close enough to that region we will continue to move closer to it forever.

Answer 8

attractor

Question 9

Two examples of attractors

Answer 9

stable equilibrium

limit cycle attractor (oscillation)

Question 10

What are the two conditions for a limit cycle attractor

Answer 10

1. the equilibrium must be an unstable spiral (must spiral outwards)
2. Somewhere in the stable spiral around that must be a stable spiral

When these conditions are met a limit cycle attracter will form sandwiched between both spirals

Question 11

___________ an equilibrium that spirals inward

Answer 11

stable spiral- spiral sink

Question 12

_______________ an equilibrium that spirals outward

Answer 12

unstable spiral- spiral source

Question 13

_________________ an equilibrium that has change vectors that point toward the equilibrium point

Answer 13

stable node (sink)

Question 14

________________ an equilibrium point with change vectors point away from equilibrium point

Answer 14

unstable node (source)

Question 15

____________ an equilibrium that has both stable and unstable tendencies. The x will be stable while y is unstable or vise versa

Answer 15

saddle point

Question 16

__________________ when two equilibrium (one stable and one unstable) get closer and closer, collide, and disappear

Answer 16

saddle node bifurcation

Question 17

______________ a type of bifurcation in which two equilibrium (one stable and one unstable) get closer, collide, swap stabilities and continue with the parameters

Answer 17

transcrital bifurcation

Question 18

_______________ a stable equilibrium becomes an unstable equilibria and two stable equilibria appear on either side

Answer 18

pitch fork bifurcation

Question 19

_____________________ of an equilibrium is the set of all points in the state space that eventually flow toward that stable point

Answer 19

Basin of attraction

Question 20

formula for the average rate of change

Answer 20

Delta X/ Delta T

Question 21

How would you find instantaneous rate of change

Answer 21

Average rate of change= Delta X/ Delta T
Use two delta T’s close to each other
Then use slope formula

Question 22

What information tells you the total value on a graph

Answer 22

the area under the curve

Question 23

How would you find the area under the curve

Answer 23

P(t)* Delta T. yen add all the values for the interval in units of delta T.

Question 24

Derivative in terms of geometry

Answer 24

slope of tangent line

Question 25

derivative in terms of change of various quantities

Answer 25

instantaneous rate of change

Question 26

name 2 conditions in which a function is not differentiable

Answer 26

1. the slope of the tangent line does not exist | 2. slope of the tangent line is vertical.

Question 27

What is the growth function

Answer 27

Poe^rt

Question 28

another growth function. Used to describe salmon

Answer 28

Por^t

Question 29

what is the derivative of ln x

Answer 29

1/x

Question 30

What is a riemann sum

Answer 30

Use delta T and add all the values from a to be together in units of delta t.

Question 31

Integrals are a more accurate version of a

Answer 31

riemann sum

Question 32

If you need to find the area under the curve take the

Answer 32

integral

Question 33

What is the logistic growth function

Answer 33

rx(1-(p/n))

Question 34

Left handed remain sum (0,5)

Answer 34

0,1,2,3,4,

Question 35

right handed remain sum (0,5)

Answer 35

1,2,3,4,5,