Bifurcation Analysis of a Railway Wheelset With Nonlinear Wheel-rail Contact

2021 ◽  
Author(s):  
Jinying Guo ◽  
Huailong Shi ◽  
Ren Luo ◽  
Jing Zeng
Keyword(s):  
Contact Angle ◽  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Critical Speed ◽  
Nonlinear Term ◽  
Linear Term ◽  
Railway Vehicle ◽  
Hopf Bifurcation Point ◽  
Quintic Polynomial ◽  
The Stability

Abstract Stability is a key factor for the operation safety of railway vehicles, while current work employs linearized and simplified wheel/rail contact to study the bifurcation mechanism and assess the stability. To study the stability and bifurcation characters under real nonlinear wheel/rail contact, a fully parameterized nonlinear railway vehicle wheelset model is built. In modeling, the geometry nonlinearities of wheel and rail profiles come from field measurements, including the rolling radius, contact angle, and curvatures, etc. Firstly, four flange force models and their effects on the stability bifurcations are compared. It shows that an exponent fitting is more proper than a quintic polynomial one to simulate the flange, and works well without changing the Hopf bifurcation type. Then the effects of each term of the nonlinear geometry of wheel/rail contact on the Hopf bifurcation and Limit Circle bifurcation are discussed. Both the linear term and nonlinear term of rolling radius have a significant influence on Hopf bifurcation and Limit Point of Circle (LPC) bifurcation. The linear critical speed (Hopf bifurcation point) and the nonlinear critical speed (LPC bifurcation point) changes times while within the calculated range of the linear term of the rolling radius. Its nonlinear term changes the bifurcation type and the nonlinear critical speed almost by half. The linear term of contact angle, the radius of curvature of wheel, and rail profile should be taken into consideration since they can change both the bifurcation point and type, while the cubic term can be ignored. Furtherly, the field measured wheel profiles for several running mileages are employed to examine the real geometry nonlinearities and the according Hopf bifurcation behavior. The result shows that a larger suspension stiffness would increase the running stability under wheel wear.

Spatiotemporal Dynamics in Reaction–Diffusion Neural Networks Near a Turing–Hopf Bifurcation Point

2019 ◽  
Vol 29 (11) ◽  
pp. 1950154 ◽  
Author(s):  
Jiazhe Lin ◽  
Rui Xu ◽  
Xiaohong Tian
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Normal Form ◽  
Bifurcation Point ◽  
Reaction Diffusion ◽  
Spatiotemporal Dynamics ◽  
Normal Form Theory ◽  
Hopf Bifurcation Point ◽  
Codimension Two ◽  
Form Theory

Since the electromagnetic field of neural networks is heterogeneous, the diffusion phenomenon of electrons exists inevitably. In this paper, we investigate the existence of Turing–Hopf bifurcation in a reaction–diffusion neural network. By the normal form theory for partial differential equations, we calculate the normal form on the center manifold associated with codimension-two Turing–Hopf bifurcation, which helps us understand and classify the spatiotemporal dynamics close to the Turing–Hopf bifurcation point. Numerical simulations show that the spatiotemporal dynamics in the neighborhood of the bifurcation point can be divided into six cases and spatially inhomogeneous periodic solution appears in one of them.

Dynamics near a symmetric Hopf bifurcation

1988 ◽  
Vol 108 (3-4) ◽  
pp. 249-267 ◽  
Author(s):  
Wayne Nagata
Keyword(s):  
Hopf Bifurcation ◽  
Differential Equations ◽  
Symmetry Breaking ◽  
Bifurcation Point ◽  
Unperturbed System ◽  
System Of Differential Equations ◽  
Hopf Bifurcation Point ◽  
Secondary Bifurcations

SynopsisWe consider the effects of a small symmetry breaking perturbation on a system of differential equations near a Hopf bifurcation point, where the unperturbed system has O(2) symmetry. We show that there exist secondary bifurcations of invariant two-tori of solutions and that the flow on the tori can be quasiperiodic or weakly resonant (phase locked), depending on the size of the perturbation.

scholarly journals Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Aming Hao ◽  
Xiaolong Li ◽  
Longhua She
Keyword(s):  
Adaptive Control ◽  
Hopf Bifurcation ◽  
Large Scale ◽  
Stability Range ◽  
Hopf Bifurcation Point ◽  
Maglev System ◽  
Large Scale Disturbance ◽  
Excited Vibration ◽  
Parameter Variance ◽  
The Stability

EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

ESTIMATION OF THE HOPF BIFURCATION POINT FOR AEROELASTIC SYSTEMS

2001 ◽  
Vol 248 (1) ◽  
pp. 31-42 ◽  
Author(s):  
A. SEDAGHAT ◽  
J.E. COOPER ◽  
A.Y.T. LEUNG ◽  
J.R. WRIGHT
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Hopf Bifurcation Point

NEURONS ARE POISED NEAR THE EDGE OF CHAOS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250098 ◽  
Author(s):  
LEON CHUA ◽  
VALERY SBITNEV ◽  
HYONGSUK KIM
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Nonlinear Differential Equations ◽  
Complex Conjugate ◽  
Excitation Current ◽  
Hopf Bifurcation Point ◽  
Synaptic Excitation ◽  
Edge Of Chaos ◽  
Subcritical Hopf Bifurcation ◽  
Dc Current

This paper shows the action potential (spikes) generated from the Hodgkin–Huxley equations emerges near the edge of chaos consisting of a tiny subset of the locally active regime of the HH equations. The main result proves that the eigenvalues of the 4 × 4 Jacobian matrix associated with the mathematically intractable system of four nonlinear differential equations are identical to the zeros of a scalar complexity function from complexity theory. Moreover, we show the loci of a pair of complex-conjugate zeros migrate continuously as a function of an externally applied DC current excitation emulating the net synaptic excitation current input to the neuron. In particular, the pair of complex-conjugate zeros move from a subcritical Hopf bifurcation point at low excitation current to a super-critical Hopf bifurcation point at high excitation current. The spikes are generated as the excitation current approaches the vicinity of the edge of chaos, which leads to the onset of the subcritical Hopf bifurcation regime. It follows from this in-depth qualitative analysis that local activity is the origin of spikes.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

2011 ◽  
Vol 225 (12) ◽  
pp. 2804-2818 ◽  
Author(s):  
A Amamou ◽  
M Chouchane
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Critical Speed ◽  
Design Parameters ◽  
Stable Limit ◽  
Non Linear ◽  
The Stability

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

FOOD WEB CHAOS WITHOUT SUBCHAIN OSCILLATORS

2005 ◽  
Vol 15 (11) ◽  
pp. 3481-3492 ◽  
Author(s):  
BRIAN BOCKELMAN ◽  
BO DENG
Keyword(s):  
Hopf Bifurcation ◽  
Singular Perturbation ◽  
Food Web ◽  
Bifurcation Point ◽  
Period Doubling ◽  
Reproductive Rate ◽  
Hopf Bifurcation Point ◽  
Parameter Values ◽  
The Web

A basic food web of four species is considered, of which there is a bottom prey X, two competing predators Y, Z on X, and a super predator W only on Y. The main finding is that population chaos does not require the existence of oscillators in any subsystem of the web. This minimum population chaos is demonstrated by increasing the relative reproductive rate of Z alone without alternating any other parameter nor any nullcline of the system. It occurs as the result of a period-doubling cascade from a Hopf bifurcation point. The method of singular perturbation is used to determine the Hopf bifurcation involved as well as the parameter values.

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