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On the Transition to Phase Synchronized Chaos
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
Erik Mosekilde, Jakob Lund Laugesen, Zhanybai T. Zhusubaliyev
The torus bifurcation curves produce a set of period doubled quasiperiodic states, and the overall result of this reconstruction of the bifurcation diagram for the anti-symmetric modes is that part of the resonance zone is invaded by different quasiperiodic modes. This includes the occurrence of phase-modulated quasiperiodicity. Let us finally note that a recent study of the transition to chaotic phase synchronization for two coupled, nearly identical two-oscillator systems (nephrons) [23] has demonstrated essentially the same bifurcation structures for synchronization into symmetric, respectively anti-symmetric states. This result applies, provided that the 1:5 or 1:4 synchronization for the internal modes of the individual oscillator remained unaffected by the coupling.
Bifurcation and Chaos
Published in Wai-Kai Chen, Feedback, Nonlinear, and Distributed Circuits, 2018
Michael Peter Kennedy, Vandenberghe Lieven
The next most complicated form of steady-state behavior is called quasiperiodicity. In state space, this corresponds to a torus (see Figure 14.5a). Although a small piece of a limit cycle in ℝ3 looks like a line, a small section of two-torus looks like a plane; a two-torus has dimension two.
Les vertus des défauts: The scientific works of the late Mr Maurice Kleman analysed, discussed and placed in historical context, with particular stress on dislocation, disclination and other manner of local material disbehaviour
Published in Liquid Crystals Reviews, 2022
The term ‘quasi-crystalline’ is a transfer from the mathematical concept of quasi-periodicity. This occurs, for example, in studying rotations in astronomy, when bodies are undergoing several different periodic motions the periods of which are incommensurate with each other. The result is a dynamical system which never quite repeats exactly.