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# [LIFESCI 30A] - Final Exam Guide - Everything you need to know! (29 pages long)

Department
Life Sciences
Course Code
LIFESCI 30A
Professor
Conley William Joseph
Study Guide
Final

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UCLA
LIFESCI 30A
FINAL EXAM
STUDY GUIDE

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LS30A Lecture 2
28 September 2016
State of a dynamical system and its state variables status/current conditions
(i.e. with pituitary gland: current level of a hormone, concentration of GNRH in
the blood, level of testosterone, etc)
or
(Insulin release, amount of glucose in the blood, level of insulin in the
bloodstream)
Steps to set up a mathematical model:
1. Identify the quantities you want to keep track of in the system (*quantities that are
changing with time).
a. Things are always changing over time (t), so time is not considered as a
changing variable
2. Assign a variable to each one of them called state variables
a. Of a population: T = number of Tuna; S = number of sharks
b. State variables are changing over time, so the variables S & T are
considered functions of time (i.e. T(t) is the number of Tuna at time t, year
t, day t, etc. S(t) = number of Sharks at time t, year t, day t, etc)
c. Usually, we’ll omit (t). Just remember that state variables are functions of
time
d. State variables must always have units
Example:
3-species food chain:
o R = # of rabbits
o F = # foxes
o L = # of Mountain Lions
o H = Level (concentration in blood) of GnRH
o P = level of FSH and LH
o G = level of estrogen and progesterone
What is the state of a system?
Not just a property of a system as a whole, but at a specific time. The state is
also changing over time.
In the shark-tuna example. If right now there are 507 tuna and 38 sharks, we’d
say the state of the system is (507 tuna, 38 sharks).
Order matters
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Take the values of all the state variables and put them into a list
Definition: The state of a system (at a particular time t) is the collection of the values of
each of the state variables put into a “list,” more accurately called a vector
If the state is 507 tuna and 38 sharks, we write this state as
_ _
| 507 | with or without the units *Note: In the textbook, vectors
| | next to it. are written like (507, 38). I will
|_ 38 _| always write them in brackets.
The state of the H-P-G system at some time might be (10, 4, 3.792)
This might mean 10 mg/dL of GnRH, 4 mg/dL FSH + LH, etc.
State Space of the sytem The set of all possible states a system could ever be in
Example: The shark-tuna system:
All possible values of T? Any real # > 0 or # = 0
All possible values of S? Any real # > 0 or # = 0
We will represent this state space graphically as
State space for H-P-G model is a 3D space. It makes a cube. States are not just a
collection of numbers, but points in a state space.
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