Positive periodic solutions for Lotka–Volterra systems with a general attack rate. (April 2020)

• Record Type: Journal Article
• Authors: Lois-Prados, Cristina; Precup, Radu
• Is Part Of: Nonlinear analysis. Volume 52(2020)
• Publication Date: 2020-04
• Subjects: Non-autonomous Lotka–Volterra system -- Hunting cooperation -- Logistic growth -- Periodic solution -- Existence -- Localization; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103024
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel'skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the functional response of predators are discussed.