Multilayered tori in a system of two coupled logistic maps |
| |
Authors: | Zhanybai T Zhusubaliyev Erik Mosekilde |
| |
Institution: | a Kursk State Technical University, Department of Computer Science, 50 Years of October Str., 94, Kursk 305040, Russia b Complex Systems Group, Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark |
| |
Abstract: | The Letter describes different mechanisms for the formation and destruction of tori that are formed as layered structures of several sets of interlacing manifolds, each with their associated stable and unstable resonance modes. We first illustrate how a three layered torus can arise in a system of two coupled logistic maps through period-doubling or pitchfork bifurcations of the saddle cycle on an ordinary resonance torus. We hereafter present two different scenarios by which a multilayered torus can be destructed. One scenario involves a cascade of period-doubling bifurcations of both the stable and the saddle cycles, and the second scenario describes a transition in which homoclinic bifurcations destroy first the two outer layers and thereafter also the inner layer of a three-layered torus. It is suggested that the formation of multilayered tori is a generic phenomenon in non-invertible maps. |
| |
Keywords: | 05 45 Xt |
本文献已被 ScienceDirect 等数据库收录! |
|