Existence of limit cycles in a three level trophic chain with Lotka–Volterra and Holling type II functional responses

Víctor Castellanos and Ramón E. Chan-López

Chaos, Solitons & Fractals, 2017, vol. 95, issue C, 157-167

Abstract: In this paper we analyze a three level trophic chain model, considering a logistic growth for the lowest trophic level, a Lotka–Volterra and Holling type II functional responses for predators in the middle and in the cusp in the chain, respectively. The differential system is based on the Leslie–Gower scheme. We establish conditions on the parameters that guarantee the coexistence of populations in the habitat. We find that an Andronov–Hopf bifurcation takes place. The first Lyapunov coefficient is computed explicitly and we show the existence of a stable limit cycle. Numerically, we observe a strange attractor and there exist evidence of the model to exhibit chaotic dynamics.

Keywords: Food chain; Leslie–Gower scheme; Stability; Andronov–Hopf bifurcation; First Lyapunov coefficient (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077916303708
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:95:y:2017:i:c:p:157-167

DOI: 10.1016/j.chaos.2016.12.011

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().