scholarly journals Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

2000 ◽  
Vol 130 (6) ◽  
pp. 1275-1291 ◽  
Author(s):  
S. A. Gourley ◽  
S. Ruan
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Comparison Principle ◽  
Distributed Delay ◽  
Energy Methods ◽  
Integral Convolution ◽  
Nicholson’S Blowflies Equation ◽  
Uniform State ◽  
Linearized Stability ◽  
Uniform Steady State

In this paper we study the diffusive Nicholson's blowflies equation. Generalizing previous works, we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible. The linearized stability of the non-zero uniform steady state is studied in detail, mainly by using the principle of the argument. Global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations. Finally, we consider what bifurcations are possible from the non-zero uniform state in the case when it is unstable.

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

2005 ◽  
Vol 461 (2061) ◽  
pp. 2701-2720 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Constitutive Law ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

scholarly journals Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
J. Y. T. Mugisha ◽  
Mark Kimathi
Keyword(s):  
Sensitivity Analysis ◽  
Antibiotic Resistance ◽  
Steady State ◽  
Global Stability ◽  
Influenza A ◽  
Pneumococcal Pneumonia ◽  
Effective Rate ◽  
Model Parameters ◽  
Saturated Treatment ◽  
Disease Free

Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0<1, the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if R0>1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.

Thermal waves and non-uniform steady state in a Fe + H2 system

1983 ◽  
Vol 38 (11) ◽  
pp. 1775-1780 ◽  
Author(s):  
V.V. Barelko ◽  
V.M. Beibutian ◽  
YU.E. Volodin ◽  
YA.B. Zeldovich
Keyword(s):  
Steady State ◽  
Thermal Waves ◽  
Uniform Steady State

scholarly journals A Discrete Model for HIV Infection with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Brahim EL Boukari ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Time Delays ◽  
Discrete Model ◽  
Distributed Delay ◽  
Continuous Model ◽  
Distributed Time Delays ◽  
A Cell ◽  
The Times ◽  
Theoretical Results

We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

Determination of global stability of steady-state solutions of a beam system with discontinuous support using manifolds∗

1996 ◽  
Vol 7 (1) ◽  
pp. 61-75 ◽  
Author(s):  
E.L.B. van de Vorst ◽  
D.H. van Campen ◽  
R.H.B. Fey ◽  
A. de Kraker
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Beam System ◽  
Steady State Solutions

scholarly journals Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Wei Zhang ◽  
Juan Zhang ◽  
Yong-Ping Wu ◽  
Li Li
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Dairy Cows ◽  
Immune Cells ◽  
Steady States ◽  
The Body ◽  
Infection Dose ◽  
The One ◽  
Immunological Threshold ◽  
Disease Free

As we all know, bacteria is different from virus which with certain types can be killed by the immune cells in the body. The brucellosis, a bacterial disease, can invade the body by indirect transmission from environment, which has not been researched by combining with immune cells. Considering the effects of immune cells, we put a minimum infection dose of brucellosis invading into the dairy cows as an immunological threshold and get a switch model. In this paper, we accomplish a thorough dynamics analysis of a SEIB switch model. On the one hand, we can get a disease-free and bacteria-free steady state and up to three endemic steady states which may be thoroughly analyzed in different cases of a minimum infection dose in a switch model. On the other hand, we calculate the basic reproduction number R0 and know that the disease-free and bacteria-free steady state is a global stability when R0<1, and the one of the endemic steady state is a conditionally global stability when R0>1. We find that different amounts of R0 may lead to different steady states of brucellosis, and considering the effects of immunology is more serious in mathematics and biology.

Transient Deformation and Flow in Bulk Metallic Glasses and Deeply Undercooled Glass Forming Liquids — A Self-Consistent Dynamic Free Volume Model

2002 ◽  
Vol 754 ◽  
Author(s):  
Sven Bossuyt ◽  
Marios D. Demetriou ◽  
William L. Johnson ◽  
A. Lindsay
Keyword(s):  
Steady State ◽  
Free Volume ◽  
Steady State Flow ◽  
Glass Forming ◽  
Volume Model ◽  
State Flow ◽  
Free Volume Model ◽  
Self Consistent ◽  
Uniform Steady State ◽  
Volume Production

ABSTRACTRecently, a self-consistent dynamic free volume model was proposed to analyze the Newtonian and non-Newtonian uniform steady-state flow data for bulk glass forming liquids such as those of the Zr-Ti-Cu-Ni-Be Vitreloy family. The model is based on the traditional free volume model of the glass transition, the Vogel-Fulcher-Tammann (VFT) equation, and a simple treatment of free volume production and annihilation during flow. It was shown that the model results in a simple one-parameter fit to extend the VFT equation for Newtonian flow to non-Newtonian uniform steady-state flow. We further extend the model to include transient uniform flow, by considering the evolution of free volume with time.

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