Discrete dynamical systems - Eigenvalue and Eigenvectors
Discrete dynamical systems
Lessons
Notes:
Assume that is diagonalizable, with linearly independent eigenvectors , and corresponding eigenvalues . Then we can write an initial vector to be:
Let's say we want to transform with matrix . Let's call the transformed vector to be . Then,
Let's say we want to keep transforming it with matrix times. Then we can generalize this to be:
This is useful because we get to know the behaviour of this equation when →.
-
Intro Lesson
Discrete Dynamical Systems Overview:
-
4.
Predator and Prey Model
Let the eagle and rabbit population at time be denoted as, where is the time in years, is the number of eagles at time , and is the number of rabbits at time (all measured in thousands). Suppose there are two equations describing the relationship between these two species:
