Permanence for a large class of planar periodic Kolmogorov systems
The author deals with a large class of planar periodic Kolmogorov systems \[ \dot x(t)= x(t)f(t, x(t),y(t)),\qquad \dot y(t)= y(t)g(t,x(t),y(t)), \] where \(f,g: \mathbb{R}\times \mathbb{R}_+^2\rightarrow \mathbb{R}\) are continuous functions which are locally Lipschitz continuous in \((x, y)\) and \(T\)-periodic in time \(t\), for some \(T>0\). Here, the author proves that the periodic Kolmogorov system (including competition, mutualism, and some classes of predator-prey systems) is permanent when the subsystems of single species have a positive global attractive periodic solution and satisfy some additional conditions. Some results in the literature are extended and completed.
scientific article; zbMATH DE number 1763483