Arnold tongues and quasiperiodicity in a prey-predator model - Rosa C.* (2009)
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.