Mosekilde, Erik1; Zhusubaliyev, Zhanybai T.2; Laugesen, Jakob L.3; Yanochkina, Olga O.2
1 Department of Physics, Technical University of Denmark2 South West State University3 Department of Structural Engineering and Materials, Technical University of Denmark
It is well-known that the transition to chaotic phase synchronization for a periodically driven chaotic oscillator of spiral type involves a dense set of saddle-node bifurcations. However, the way of formation and precise organization of these saddle node bifurcation curves have only recently been examined in detail. By following the development of the phase portrait for the stable and unstable resonance cycles of a forced Rossler system, we demonstrate a variety of processes involved in the formation, reconstruction and final breakdown of complex multi-layered tori. A detailed bifurcation analysis also allows us both to describe the mechanisms that ensure that the regions of existence of the different resonance modes remain bounded and to show how dense sets of saddle node bifurcations accumulate along the edges of the resonance zone. (C) 2012 Elsevier Ltd. All rights reserved.
Chaos, Solitons and Fractals, 2013, Vol 46, p. 28-37