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

 
Opuscula Mathematica

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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  • 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
  • Received: 2008-01-31.
  • Revised: 2008-07-07.
  • Accepted: 2008-07-07.
Opuscula Mathematica - cover

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

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