Opuscula Mathematica
Opuscula Math. 28, no. 4 (2008), 567-592

Chaotic dynamics in the Volterra predator-prey model via linked twist maps

Marina Pireddu
Fabio Zanolin
Abstract. We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator-prey model with a periodic harvesting. The proof relies on some recent results about chaotic planar maps combined with the study of geometric features which are typical of linked twist maps.
Keywords: Volterra predator-prey system, harvesting, periodic solutions, subharmonics, chaotic-like dynamics, topological horseshoes, linked twist maps.
Mathematics Subject Classification: 34C25, 37E40, 92C20.
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About the authors ▼
Marina Pireddu
University of Udine, Department of Mathematics and Computer Science, via delle Scienze 206, I-33100 Udine, Italy
Fabio Zanolin
University of Udine, Department of Mathematics and Computer Science, via delle Scienze 206, I-33100 Udine, Italy
About the article ▼
Received: 2008-01-31.
Revised: 2008-07-07.
Accepted: 2008-07-07.
Cite this article as ▼
Marina Pireddu, Fabio Zanolin, Chaotic dynamics in the Volterra predator-prey model via linked twist maps, Opuscula Math. 28, no. 4 (2008), 567-592, http://dx.doi.org/10.7494/OpMath.2008.28.4.567.
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