Arnold tongues and quasiperiodicity in a prey-predator model

• Main Author: Rosa C.*
• Publication Date: 2009
• Other Authors: Correia M.J.*, Rech P.C.*
• Format: Article
• Language: eng
• Source: Repositório Institucional da Udesc
• dARK ID: ark:/33523/0013000004b6r
• Download full: https://repositorio.udesc.br/handle/UDESC/9931

We consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via analytical and numerical simulations, phenomena associated with the appearance, in the parameter-space, of structures like Arnold tongues involved in the Naimark-Sacker bifurcation. We determine analytically the location of the parameter sets where Naimark-Sacker bifurcation occurs, and the location on this line where tongues of arbitrary period are born. Lyapunov exponents, bifurcation diagrams, parameter-space and phase-space diagrams are used to show the transition from quasiperiodic to chaotic states. © 2007 Elsevier Ltd. All rights reserved.