scholarly journals The Influence of Circulatory Forces on the Stability of Undamped Gyroscopic Systems

2021 ◽  
pp. 90-94
Author(s):  
Ubong D. Akpan
Keyword(s):  
Lyapunov Method ◽  
Eigenvalue Method ◽  
The Stability ◽  
Gyroscopic Systems

In this paper, the effects of circulatory forces on undamped gyroscopic systems have been studied. The stability or otherwise of arising MGKN systems have been analysed using eigenvalue method and Lyapunov method. Bottema-Lakhadanov-Karapetyan theorem is also employed to further analyze the systems. Examples are given to illustrate the use of these methods in determining the stability or otherwise of undamped gyroscopic circulatory systems.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

Stability of carbon monoxide oxidation process on gold nanoparticles

2020 ◽  
Vol 8 (1) ◽  
pp. 116-124
Author(s):  
P. P. Kostrobij ◽  
◽  
I. A. Ryzha ◽  
Keyword(s):  
Carbon Monoxide ◽  
Gold Nanoparticles ◽  
Reaction Mechanisms ◽  
Structural Changes ◽  
Oxidation Process ◽  
Lyapunov Method ◽  
Catalyst Surface ◽  
Carbon Monoxide Oxidation ◽  
One Step ◽  
The Stability

The stability conditions for mathematical models of carbon monoxide oxidation on the surface of gold nanoparticles are investigated. The cases of reaction mechanisms of one-step and step-by-step transformation of reagents are consecutively considered. Using the stability analysis by Lyapunov method, it is shown that models which take into account the possibility of structural changes of the catalyst surface can predict the occurrence of oscillatory mode in the system as a result of Hopf instability.

Uniform robust exact differentiator based adaptive robust control for a class of nonlinear systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2901-2911 ◽  
Author(s):  
Zhangbao Xu ◽  
Dawei Ma ◽  
Jianyong Yao
Keyword(s):  
Robust Control ◽  
Nonlinear Systems ◽  
Closed Loop ◽  
Lyapunov Method ◽  
Adaptive Robust Control ◽  
Experimental Results ◽  
Closed Loop System ◽  
Robust Controller ◽  
Performance Simulation ◽  
The Stability

In this paper, an adaptive robust controller with uniform robust exact differentiator has been proposed for a class of nonlinear systems with structured and unstructured uncertainties. The adaptive robust controller is integrated with an uniform robust differentiator to handle the problem of the incalculable part of the derivative of virtual controls and the differential explosion happened in backstepping techniques. The stability of the closed loop system is demonstrated via Lyapunov method ensuring a prescribed transient and tracking performance. Simulation and experimental results are carried out to verify the advantages of the proposed method.

scholarly journals Design of Augmented Nonlinear PD Controller of Delta/Par4-Like Robot

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Amjad J. Humaidi ◽  
Ahmed Ibraheem Abdulkareem
Keyword(s):  
Trajectory Tracking ◽  
Lyapunov Method ◽  
Dynamic Performance ◽  
Parallel Robot ◽  
Pd Controller ◽  
Comparison Study ◽  
Tracking Accuracy ◽  
Control Schemes ◽  
The Stability ◽  
Made In

This work presents the design of two control schemes for a Delta/Par4-like parallel robot: augmented PD (APD) controller and augmented nonlinear PD (ANPD) controller. The stability of parallel robot based on nonlinear PD controller has been analyzed and proved based on Lyapunov method. A comparison study between APD and ANPD controllers has been made in terms of performance and accuracy improvement of trajectory tracking. Also, another comparison study has been presented between augmented nonlinear PD (ANPD) controller and nonaugmented nonlinear PD (NANPD) controller in order to show the enhancement of introducing the augmented structure on dynamic performance and trajectory tracking accuracy. The effectiveness of augmented PD controllers (APD and ANPD) and nonaugmented nonlinear PD (NANPD) controller for the considered parallel robot are verified via simulation within the MATLAB environment.

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