Non-autonomous dynamics of a semi-Kolmogorov population model with periodic forcing. (October 2016)

• Record Type: Journal Article
• Authors: Caraballo, Tomás; Colucci, Renato; Han, Xiaoying
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 661
• Page End: 680
• Publication Date: 2016-10
• Subjects: Nonautonomous dynamical system -- Population dynamics -- Pullback attractor; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.03.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study a semi-Kolmogorov type of population model, arising from a predator–prey system with indirect effects. In particular we are interested in investigating the population dynamics when the indirect effects are time dependent and periodic. We first prove the existence of a global pullback attractor. We then estimate the fractal dimension of the attractor, which is done for a subclass by using Leonov's theorem and constructing a proper Lyapunov function. To have more insights about the dynamical behavior of the system we also study the coexistence of the three species. Numerical examples are provided to illustrate all the theoretical results.