Opuscula Math. 28, no. 4 (2008), 567-592
Chaotic dynamics in the Volterra predator-prey model via linked twist maps
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.