Repetitive activity of a molluscan neurone driven by maintained currents: A supercritical bifurcation

1981 ◽  
Vol 42 (2) ◽  
pp. 79-85 ◽  
Author(s):  
A. V. Holden ◽  
S. M. Ramadan
Keyword(s):  
Supercritical Bifurcation ◽  
Molluscan Neurone

Dynamics of a Cleaning Blade Based on a 2DOF Link Model

2009 ◽  
Author(s):  
Yoshinori Inagaki ◽  
Tsuyoshi Nohara ◽  
Go Kono ◽  
Minoru Kasama ◽  
Masatsugu Yoshizawa
Keyword(s):  
Amplitude Equation ◽  
Laser Printer ◽  
Small Disturbance ◽  
Governing Equations ◽  
Supercritical Bifurcation ◽  
Narrow Region ◽  
Hamiltonian Hopf Bifurcation ◽  
Excited Vibration ◽  
Link Model ◽  
Unstable Vibration

To analyze the dynamics of a cleaning blade in a laser printer, observation of the vibration of the cleaning blade and analysis of a 2DOF model have been carried out. First, from the observation of the vibration of the actual cleaning blade, the stationary self-excited vibration has been confirmed. Next, a 2DOF model has been presented and its governing equations have been derived. The bottom of the model is assumed to always contact a floor surface, and the friction coefficient is constant and not dependent on the floor velocity. Third, by solving the equations governing the motion of the 2DOF model, five patterns of static equilibrium states have been obtained. Moreover it has been clarified from linear stability analysis that one of five patterns corresponds to the shape of the cleaning blade and is unstable for a small disturbance in a narrow region. This unstable vibration is a bifurcation classified as Hamiltonian-Hopf bifurcation. Fourth, by keeping up to the 3rd order terms, the nonlinear complex amplitude equation has been obtained, and the steady amplitude can be decided. As a result, the steady amplitude has been determined as the products of the 2nd order terms. Furthermore it has been clarified that such a self-excited vibration is classified as the supercritical bifurcation.

Intelligent PID Control and the Bifucation Behavior of Hydrogenerator Set

2014 ◽  
Vol 494-495 ◽  
pp. 1702-1705
Author(s):  
Zhong Liao ◽  
Chun Dan Song
Keyword(s):  
Pid Control ◽  
Complex Dynamics ◽  
Intelligent System ◽  
Nonlinear Differential Equations ◽  
Nonlinear Dynamical ◽  
Supercritical Bifurcation ◽  
Set Systems ◽  
Highly Nonlinear ◽  
Intelligent Pid ◽  
Bifurcation Behavior

.Considering of the highly nonlinear, time-variable and complex dynamics and the easy variance of hydrogenerator set systems structure and parameters, a nonlinear dynamical model is presented, which can be analyzed by the bifurcation theory of nonlinear differential equations and simulated in computer. By using the genetic algorithm, the PID parameters of hydrogenerator set intelligent system are optimized and the control performances are improved. The algebra criterion about the existence of bifurcation is employed to study the bifurcation behavior of the nonlinear model which takes the PID parameters as the bifurcation ones. The simulations show that a supercritical bifurcation is likely to exist in hydrogenerator set system and the bifurcation will occur for the higher values of PID parameters. Theory and simulation results of this paper can be considered as good suggest for intelligent PID control system of hydrogenerator set system.

Weakly nonlinear theory of shear-banding instability in a granular plane Couette flow: analytical solution, comparison with numerics and bifurcation

2010 ◽  
Vol 666 ◽  
pp. 204-253 ◽  
Author(s):  
PRIYANKA SHUKLA ◽  
MEHEBOOB ALAM
Keyword(s):  
Couette Flow ◽  
Shear Banding ◽  
Base Flow ◽  
Plane Couette Flow ◽  
Weakly Nonlinear ◽  
Subcritical Bifurcation ◽  
Supercritical Bifurcation ◽  
Weakly Nonlinear Theory ◽  
Pitchfork Bifurcations ◽  
The Mean

A weakly nonlinear theory, in terms of the well-known Landau equation, has been developed to describe the nonlinear saturation of the shear-banding instability in a rapid granular plane Couette flow using the amplitude expansion method. The nonlinear modes are found to follow certain symmetries of the base flow and the fundamental mode, which helped to identify analytical solutions for the base-flow distortion and the second harmonic, leading to an exact calculation of the first Landau coefficient. The present analytical solutions are used to validate a spectral-based numerical method for the nonlinear stability calculation. The regimes of supercritical and subcritical bifurcations for the shear-banding instability have been identified, leading to the prediction that the lower branch of the neutral stability contour in the (H, φ0)-plane, where H is the scaled Couette gap (the ratio between the Couette gap and the particle diameter) and φ0 is the mean density or the volume fraction of particles, is subcritically unstable. The predicted finite-amplitude solutions represent shear localization and density segregation along the gradient direction. Our analysis suggests that there is a sequence of transitions among three types of pitchfork bifurcations with increasing mean density: from (i) the bifurcation from infinity in the Boltzmann limit to (ii) subcritical bifurcation at moderate densities to (iii) supercritical bifurcation at larger densities to (iv) subcritical bifurcation in the dense limit and finally again to (v) supercritical bifurcation near the close packing density. It has been shown that the appearance of subcritical bifurcation in the dense limit depends on the choice of the contact radial distribution function and the constitutive relations. The scalings of the first Landau coefficient, the equilibrium amplitude and the phase diagram, in terms of mode number and inelasticity, have been demonstrated. The granular plane Couette flow serves as a paradigm that supports all three possible types of pitchfork bifurcations, with the mean density (φ0) being the single control parameter that dictates the nature of the bifurcation. The predicted bifurcation scenario for the shear-band formation is in qualitative agreement with particle dynamics simulations and the experiment in the rapid shear regime of the granular plane Couette flow.

scholarly journals Mathematical Analysis of the Concomitance of Illicit Drug Use and Banditry in a Population

2021 ◽  
Author(s):  
John Olajide Akanni ◽  
Afeez Abidemi
Keyword(s):  
Drug Use ◽  
Illicit Drug ◽  
Illicit Drug Use ◽  
Control Measures ◽  
Dynamical System Theory ◽  
Theory Approach ◽  
Supercritical Bifurcation ◽  
Spread Dynamics ◽  
Quantitative Results ◽  
The Impact

Abstract One of the majors global health and social problem facing the world today is the use of illicit drug and the act banditry. The two problems have resulted into lost of precious lives, properties and even a devastating effects on the economy of some countries where such acts were been practiced. Of interest in this work is to study the global stability of illicit drug use spread dynamics with banditry compartment using a dynamical system theory approach. Illicit drug use and banditry reproduction number was evaluated analytically, which measures the potential spread of the illicit drug use and banditry in the population. The system exhibits supercritical bifurcation property, telling us that local stability of an illicit drug and banditry-present equilibrium exist and it is unique. In addition, the illicit drug and banditry-free and illicit drug and banditry-present equilibria were shown to be global asymptotically stable, this was achieved by construction of suitable Lyapunov functions. Sensitivity analysis was carried out to know the impact of each parameter on the dynamical spread of illicit drug use and banditry in a population. Numerical simulations were used to validate the obtained quantitative results, and examine the effects of some key parameters on the system. It was discovered that, to reduce the burden of banditry in the population, stringent control measures must be put in place to reduce the use of illicit drug in a population. Suggested control measures to use in curtail the menace of the illicit drug use and banditry were recommends.

scholarly journals IMPACT OF DOWNSTREAM POTENTIAL PERTURBATIONS ON THE NONLINEAR STABILITY OF A GENERIC FAN

2020 ◽  
Vol 4 ◽  
pp. 217-225
Author(s):  
David Romera ◽  
Roque Corral
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Static Pressure ◽  
Maximum Amplitude ◽  
Nonlinear Stability Analysis ◽  
Aerodynamic Stability ◽  
Nodal Diameter ◽  
Fourier Decomposition ◽  
Supercritical Bifurcation ◽  
Nonlinear Contribution

The dependence of the aerodynamic stability of fan blades with amplitude and nodal diameter of potential perturbations associated with the presence of pylons is studied. The analysis is conducted using a novel block-wise spatial Fourier decomposition of the reduced-passages to reconstruct the full-annulus solution. The method represents very efficiently unsteady flows generated by outlet static pressure non-uniformities. The explicit spatial Fourier approximation is exploited to characterize the relevance of each nodal diameter of outlet perturbations in the fan stall process, and its nonlinear stability is studied in a harmonic by harmonic basis filtering the nonlinear contribution of the rest. The methodology has been assessed for the NASA rotor 67. The maximum amplitude of the downstream perturbation at which the compressor becomes unstable and triggers a stall process has been mapped. It is concluded that the fan stability dependence with the amplitude of the perturbation is weaker than in the case of intake distortion. For perturbations with an odd number of nodal diameters, the nonlinear stability analysis leads to the same conclusions as to the small amplitude linear stability analysis. However, if the perturbations have an even number nodal diameters, the flow exhibits a supercritical bifurcation and have a stabilizing effect.

Experimental Verification of Subcritical Whirl Bifurcation of a Rotor Supported on a Fluid Film Bearing

1998 ◽  
Vol 120 (3) ◽  
pp. 605-609 ◽  
Author(s):  
J. C. Deepak ◽  
S. T. Noah
Keyword(s):  
Limit Cycle ◽  
Journal Bearing ◽  
Gradual Increase ◽  
Fluid Film ◽  
Subcritical Bifurcation ◽  
Supercritical Bifurcation ◽  
Fluid Film Bearings ◽  
Unbalanced Rotor ◽  
Single Disk ◽  
Sudden Jump

The paper presents the results of the experiments that were conducted on a short fluid film bearing with a simple single disk rotor. The behavior of the journal was analyzed as a function of the rotor system parameters such as the load, speed, and imbalance mass. It was verified that the journal bearing can lose stability through either a subcritical or a supercritical bifurcation. In the supercritical bifurcation, the expected gradual increase in the amplitude of the limit cycle was observed, while in the subcritical bifurcation there was a sudden jump to a large limit cycle. In the case of a subcritical bifurcation, it was also observed that the journal bearing became unstable below the rotor threshold speed of instability, following a small perturbation applied to the rotor. Demarcations were made for the stable regions of operation (regions where the rotor is stable below the threshold speed of instability) for the journal bearing based on the obtained experimental results. Experiments were also performed to analyze the effects of imbalance of the rotor on the threshold speed of instability. It was observed that the flexible unbalanced rotor had a lower threshold speed of instability. The limitations of the linear theory of fluid film bearings in predicting these phenomena are discussed.

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