Connection to a Disjointed Path using a Complex Bifurcation Solution

2009 ◽  
Author(s):  
T. Manabe ◽  
M. Kanazawa ◽  
N. Tosak
Keyword(s):  
Bifurcation Solution

Data Processing in Bifurcation Analysis of Maps with Time-Delays in the Frequency Domain

2014 ◽  
Vol 685 ◽  
pp. 634-637
Author(s):  
Li Zeng ◽  
Jun Wei Wang
Keyword(s):  
Data Processing ◽  
Frequency Domain ◽  
Time Delays ◽  
Period Doubling ◽  
Feedback Systems ◽  
Bifurcation Solution ◽  
Nonlinear Maps ◽  
The Stability ◽  
Frequency Domain Approach ◽  
Period Doubling Bifurcations

A unified frequency-domain approach to analyze the NS (Neimark-Sacker) bifurcations and the period-doubling bifurcations of nonlinear maps with time-delays in the linear feed-forward term is presented. The technique relies on the HBA (harmonic balance approximation, a very important method in data processing ) and feedback systems theory. The expressions of the bifurcation solution and the stability are derived.

Out-of-Plane Solutions and Bifurcations of Submersibles in Free Positive Buoyancy Ascent

1994 ◽  
Vol 38 (04) ◽  
pp. 259-271
Author(s):  
Fotis A. Papoulias ◽  
Ibrahim Aydin
Keyword(s):  
Degrees Of Freedom ◽  
Pitchfork Bifurcation ◽  
Control Surface ◽  
Geometric Properties ◽  
Six Degrees Of Freedom ◽  
Out Of Plane ◽  
Bifurcation Solution ◽  
Extreme Sensitivity ◽  
And Control ◽  
Surface Deflections

The problem of motion stability of submersible vehicles in free positive buoyancy ascent is analyzed. Motion is allowed to occur in combined vertical and horizontal planes. Continuation and catastrophe theory techniques are employed to trace all possible steady-state solutions in six degrees of freedom, while local linearization reveals their stability properties. Vehicle geometric properties and control surface deflections are used as the primary bifurcation parameters. It is shown that multiple solutions may exist in the form of pitchfork bifurcation, solution separation, hysteresis, and teardrop branches. Regions in parameter spaces are identified where extreme sensitivity of solutions to geometric properties and hydrodynamic modeling is present.

Bifurcation Analysis of Nonlinear Vibration Isolation System With Hard Stiffness by Cell Mapping

2003 ◽  
Author(s):  
Xiang Yu ◽  
Shijian Zhu ◽  
Jingjun Lou
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Mapping Method ◽  
Cell Mapping ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Bifurcation Solution ◽  
Numerical Research

Period-doubling bifurcation is one of the major routes to chaos, but the methods widely used have some shortages in analyzing the bifurcation of the nonlinear vibration isolation system with hard stiffness. The location and property of bifurcation solution can be obtained conveniently by using numerical methods. Therefore, numerical research is important. In this paper, global bifurcation diagram is achieved by using Poincare´ mapping method. Subsequently, cell mapping as a useful numerical method is applied to analyze the static and dynamic bifurcation of nonlinear vibration isolation system with hard stiffness.

On conical swirling flows in an infinite fluid

1994 ◽  
Vol 276 ◽  
pp. 261-271 ◽  
Author(s):  
C. Sozou ◽  
L. C. Wilkinson ◽  
V. N. Shtern
Keyword(s):  
Kinematic Viscosity ◽  
Axisymmetric Flow ◽  
Meridional Flow ◽  
Swirling Flows ◽  
Polar Coordinate System ◽  
Axial Component ◽  
Line Density ◽  
Polar Coordinate ◽  
Bifurcation Solution ◽  
Infinite Line

The steady axisymmetric flow generated in an unbounded incompressible viscous fluid, of density ρ and kinematic viscosity v, by torque-producing singularities with constant line density c along the semi-infinite line θ = 0 of a spherical polar coordinate system (r, θ, ϕ) that was investigated by Paull & Pillow (1985b), is reconsidered. The numerical solution constructed revealed the following features. (i) For values of c up to about 46.9 there is only one solution where the axial component of the meridional flow is directed from θ = 0 to θ = π. This solution can be continued to all values of c. (ii) For c > 46.9 the system of equations allows bifurcation and two more solutions with a single separatrix are possible. (iii) For c = ∞ one of the two branches of the separatrix asymptotes to θ = ½π and the other to θ = π. The asymptotic solution for large c constructed by Paull & Pillow (1985b), where the meridional flow consists of two colliding flows, relates to the bifurcation solution where the separatrix asymptotes to ½π as c → ∞.

Sign in / Sign up

Export Citation Format

Share Document