In this paper, applying the Horn's fixed point theorems in Banach spaces we obtain a theorem of existence of positive periodic solutions for periodic Kolmogorov type systems with delays. As the applications of this theorem, we study the existence of positive periodic solutions for some periodic Lotka--VOlterra type systems with delays and establish new and practical distinguishing criteria.
In this paper, we study two species time-delayed predator–prey Lotka–Volterra type dispersal systems with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this systems are established. The theoretical results are confirmed by a special example and numerical simulations.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.