We prove the existence of in nitely 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
Pireddu, M., Zanolin, F. (2008). Chaotic dynamics in the Volterra predator-prey model via linked twist maps. OPUSCULA MATHEMATICA. ROCZNIK AKADEMIA GÓRNICZO-HUTNICZA IM. STANISłAWA STASZICA, 28/4, 567-592.
Chaotic dynamics in the Volterra predator-prey model via linked twist maps
PIREDDU, MARINA;
2008
Abstract
We prove the existence of in nitely 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
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