Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2010-05-22
Journal of Differential Equations, 248, 1955-1971 (2010)
Biology
Quantitative Biology
Populations and Evolution
Scientific paper
The dynamics of interacting structured populations can be modeled by $\frac{dx_i}{dt}= A_i (x)x_i$ where $x_i\in \R^{n_i}$, $x=(x_1,\dots,x_k)$, 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 $\lambda_i(\mu)$ of the $A_i(x)$ with respect to invariant measures $\mu$. The necessary condition requires $\max_i \lambda_i(\mu)>0$ 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 $\max_i \lambda_i(\mu)>0$ for all invariant measures $\mu$ 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.
Hofbauer Josef
Schreiber Sebastian J.
No associations
LandOfFree
Robust permanence for interacting structured populations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Robust permanence for interacting structured populations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Robust permanence for interacting structured populations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-590315