10/12  Notes for COSC 681 lecture part

Chapter 1 and 2 are *extremely* important in understanding what can be done in science
and how complex systems are described.  Appropriate to read with your feet up and your
doggie/kitty next to you.

Chapter 3:
p 30 basic equation that describes state time series

p 31 phase space example

p 33 at each point, array shows the next state (i.e., time going forward)
attractor:  converging point -- no outgoing arrows
basic of attraction (for each attractor): set of all initial states that end up at the attractor
stability: converging -- stable
           diverging -- unstable
           
p 33 Do Exercise 3.6

Chapter 4:
p 35  the equation for state variable x

p 36 definition of time series

p 36 Do exercise 4.1, 4.2 and draw phase space

p 36 -37 definitions of linear/non-linear
                        first order/higher order
                        autonomous/non-autonomous

p 41 Code 4.4  Note the initialize, loop (update(), calculate statistics())

p 41 - 45 -- demo the python code running

p 46-47  need to be careful when updating states

p 47 - 50 -- demo the python code running