Note: If you wish to use any of the libraries noted below, then you will need to copy and paste the following commands in R first:

install.packages("install.load") # install the install.load package
# you will need to have GNU Octave (check the RcppOctave CRAN page for more details) installed on your system, then you can use the code below:
install.load::install_load("ramify", "pracma") # install and load the named packages and all of their dependencies, including the extra system dependencies (this process may take a while depending on the number of dependencies)





# Alternatively, if you already have the packages installed, then you can follow these steps:
install.packages("install.load") # install the install.load package
install.load::load_package("ramify", "pracma") # load the packages



Examples from Tennessee State University Applied Math for Engineers graduate-level course, Spring 2012

Example 1

Example 2

For the following state equations plot y versus x for the following initial conditions: [1, 1, 1]’, [1, 2, 1]’, [1, 5, 1]’, [1, 10, 1]’, [10, 2, 1]’, [10, 5, 1]’, [10, 10, 1]’

\[\dot{x} (t) = −y(t) − z(t)\] \[\dot{y} (t) = x(t) + ay(t)\] \[\dot{z} (t) = b + z(t)(x(t) − c)\]

Where a = b = 0.2 and c = 5.7

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