To understand the mechanisms underlying species coexistence, ecologists often study
invasion growth rates of theoretical and data-driven models. These growth rates correspond …

We present a sufficient condition for robust permanence of ecological (or Kolmogorov)
differential equations based on average Liapunov functions. Via the minimax theorem we …

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and
Nonautonomous Parabolic Equations and Applications focuses on the principal spectral …

9 Kolmogorov and population dynamics Page 1 9 Kolmogorov and population dynamics Karl
Sigmund Faculty for Mathematics, University of Vienna, and International Institute for Applied …

The paper is concerned with the question of smoothness of the carrying simplex S for a
discrete-time dissipative competitive dynamical system. We give a necessary and sufficient …

The dynamics of interacting structured populations can be modeled by dxidt= Ai (x) xi where
[Formula: see text], x=(x1,…, xk), and Ai (x) are matrices with non-negative off-diagonal …

This paper deals with global asymptotic behaviour of the dynamics for N-dimensional
competitive Kolmogorov differential systems of equations $\frac {\mathrm {d}{x} _ {i}}{\mathrm …

For competitive Lotka–Volterra systems, Ahmad and Lazer's work [S. Ahmad, AC Lazer,
Average growth and total permanence in a competitive Lotka–Volterra system, Annali di …

We consider ecological difference equations of the form x_t+1^i=x_t^iA_i(x_t), where x_t^i is
a vector of densities corresponding to the subpopulations of species i (eg, subpopulations of …

In this paper, we first consider an N-dimensional system slightly more general than the Lotka–
Volterra system, and give conditions that imply strong persistence of all species. Using this …