Fibonacci numbers: A population dynamics perspective.

Fibonacci numbers or Fibonacci sequence is among the most popular numbers or sequence in Mathematics. In this paper, we discuss the sequence in a population dynamics perspective. We discuss the early development of the sequence and interpret the sequence as a number of a hypothetical population. The governing equation that produces the Fibonacci sequence is written in a matrix form having a square matrix . We show the relation of the eigenvalues, eigenvectors, and eigenspaces to the matrix with the dynamics of the sequence. We also generalize the matrix equation so that it governs a more realistic model of the hypothetical population. Some results regarding the modified golden ratio are presented.