scholarly journals Global secondary bifurcation, symmetry breaking and period-doubling

2019 ◽  
pp. 1 ◽  
Author(s):  
Rainer Mandel
Keyword(s):  
Symmetry Breaking ◽  
Period Doubling ◽  
Secondary Bifurcation

Symmetry breaking and period doubling on a torus in the VLF regime in Taylor-Couette flow

1996 ◽  
Vol 54 (5) ◽  
pp. 4938-4957 ◽  
Author(s):  
J. von Stamm ◽  
U. Gerdts ◽  
Th. Buzug ◽  
G. Pfister
Keyword(s):  
Symmetry Breaking ◽  
Couette Flow ◽  
Period Doubling ◽  
Taylor Couette ◽  
Taylor Couette Flow

PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

2005 ◽  
Vol 15 (04) ◽  
pp. 1267-1284 ◽  
Author(s):  
V. AVRUTIN ◽  
M. SCHANZ
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
One Dimensional ◽  
Poincaré Return Map ◽  
Smooth Dynamical System

In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period-doubling bifurcation scenario. This scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border collision bifurcation and a pitchfork bifurcation. The mechanism leading to this scenario and its characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors, are investigated.

GROUP THEORETICAL MODE INTERACTIONS WITH DIFFERENT SYMMETRIES

1994 ◽  
Vol 04 (01) ◽  
pp. 177-191 ◽  
Author(s):  
KARIN GATERMANN ◽  
BODO WERNER
Keyword(s):  
Group Theory ◽  
Symmetry Breaking ◽  
Irreducible Representations ◽  
Bifurcation Points ◽  
Mode Interactions ◽  
Different Types ◽  
Secondary Bifurcation ◽  
Two Parameter ◽  
Symmetry Breaking Bifurcation

In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the inner-connectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.

ROBUST METHOD FOR EXPERIMENTAL BIFURCATION ANALYSIS

2002 ◽  
Vol 12 (08) ◽  
pp. 1909-1913 ◽  
Author(s):  
GERRIT LANGER ◽  
ULRICH PARLITZ
Keyword(s):  
Symmetry Breaking ◽  
Bifurcation Analysis ◽  
Duffing Oscillator ◽  
Period Doubling ◽  
Robust Method ◽  
Periodically Driven ◽  
Experimental Systems ◽  
Saddle Node ◽  
Electronic Implementation

We present a robust method to locate and continue period-doubling, saddle-node and symmetry-breaking bifurcations of periodically driven experimental systems. The method is illustrated from results obtained for an electronic implementation of a Duffing oscillator.

Transition to chaos in a two-sided collapsible channel flow

2021 ◽  
Vol 926 ◽  
Author(s):  
Qiuxiang Huang ◽  
Fang-Bao Tian ◽  
John Young ◽  
Joseph C.S. Lai
Keyword(s):  
Symmetry Breaking ◽  
Channel Flow ◽  
Period Doubling ◽  
External Pressure ◽  
Immersed Boundary ◽  
Limit Cycle Oscillation ◽  
External Pressures ◽  
Wide Range ◽  
Cycle Oscillation ◽  
The Stability

The nonlinear dynamics of a two-sided collapsible channel flow is investigated by using an immersed boundary-lattice Boltzmann method. The stability of the hydrodynamic flow and collapsible channel walls is examined over a wide range of Reynolds numbers $Re$ , structure-to-fluid mass ratios $M$ and external pressures $P_e$ . Based on extensive simulations, we first characterise the chaotic behaviours of the collapsible channel flow and explore possible routes to chaos. We then explore the physical mechanisms responsible for the onset of self-excited oscillations. Nonlinear and rich dynamic behaviours of the collapsible system are discovered. Specifically, the system experiences a supercritical Hopf bifurcation leading to a period-1 limit cycle oscillation. The existence of chaotic behaviours of the collapsible channel walls is confirmed by a positive dominant Lyapunov exponent and a chaotic attractor in the velocity-displacement phase portrait of the mid-point of the collapsible channel wall. Chaos in the system can be reached via period-doubling and quasi-periodic bifurcations. It is also found that symmetry breaking is not a prerequisite for the onset of self-excited oscillations. However, symmetry breaking induced by mass ratio and external pressure may lead to a chaotic state. Unbalanced transmural pressure, wall inertia and shear layer instabilities in the vorticity waves contribute to the onset of self-excited oscillations of the collapsible system. The period-doubling, quasi-periodic and chaotic oscillations are closely associated with vortex pairing and merging of adjacent vortices, and interactions between the vortices on the upper and lower walls downstream of the throat.

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