Fibonacci numbers: A population dynamics perspective

摘要

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 A. 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.