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Robust Permanence for Interacting Structured Populations by Josef Hofbauer; Sebastian J. Schreiber is a Mathematics article available to read on EtoBox.

What is Robust Permanence for Interacting Structured Populations about?

The dynamics of interacting structured populations can be modeled by ), and A i (x) are matrices with non-negative off-diagonal entries. These models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of A i (x). Necessary and sufficient conditions for robust permanence are derived using dominant Lyapunov exponents λ i (μ) of the A i (x) with respect to invariant measures μ. The necessary condition requires max i λ i (μ) > 0 for all ergodic measures with support in the boundary of the non-negative cone. The sufficient condition requires that the boundary admits a Morse decomposition such that max i λ i (μ) > 0 for all invariant measures μ supported by a component of the Morse decomposition. When the Morse components are Axiom A, uniquely ergodic, or support all but one population, the necessary and sufficient conditions are equivalent. Applications to spatial ecology, epidemiology, and gene networks are given.

Who reads Robust Permanence for Interacting Structured Populations?

Author

Josef Hofbauer; Sebastian J. Schreiber

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-0396)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)