Eigenvalue Analysis of a Discrete Ecology Model
Consider a discrete ecology model where the dynamics of a population are described by the following 3 \(\times\) 3 transition matrix: \[ A = \begin{pmatrix} 0.5 & 0.3 & 0.2 \\ 0.2 & 0.5 & 0.3 \\ 0.3 & 0.2 & 0.5 \end{pmatrix} \] Each entry \(a_{ij}\) represents the probability of transition from category \(j\) […]
Population Model Stability via Eigenanalysis
A population is divided into two stages: juveniles and adults. The dynamics of the population are modeled by the following transition matrix: \(A = \begin{pmatrix} 0.7 & 0.3 \\ 0.4 & 0.6 \end{pmatrix}\). (a) Find the eigenvalues of \(A\) by solving the characteristic equation \(\det(A – \lambda I) = 0\). (b) Identify the dominant eigenvalue […]