Relative entropy and discrete Poincaré inequalities for reducible matrices

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

“…The general theory explicitly describing behaviour of systems with reducible transition matrices seems to be hard to achieve due to a complicated internal structure they may have, see, e.g. [7]. However, in the structured population models considered here, we only consider matrices C that describe migration and, as mentioned before, the principle of conservation of the total population yields that they are Kolmogorov matrices.…”

Singularly perturbed population models with reducible migration matrix 1. Sova-Kurtz theorem and the convergence to the aggregated model

“…Furthermore, if l ≥ m + 1, then in each column at least one of the matrices A general theory explicitly describing behaviour of systems with reducible ML matrices seems to be unavailable due to their complicated internal structure, see e.g. [8]. Fortunately, the matrices with a positive eigenvector, such as the Kolmogorov matrices considered here, have much simpler structure.…”