scholarly journals A deterministic model for (n = 2) competitive products in a market system

2011 ◽  
Vol 10 (2) ◽  
Author(s):  
M Kekana ◽  
O Makinde
Keyword(s):  
Deterministic Model ◽  
Numerical Verification ◽  
Market System ◽  
Personal Interaction ◽  
Analytical Results ◽  
Immigration And Emigration ◽  
The Stability ◽  
Competitive Products

We proposed a new deterministic model for the dynamics of two competitive products in a given market system. The model was analyzed qualitatively to determine the stability of its equilibrium under the influence of factors such as advertisement, personal interaction, immigration and emigration. Numerical verification of the analytical results is performed and presented graphically.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

scholarly journals MODELING KENYA’S DOMESTIC RADICALIZATION LIKE A DISEASE BY INCORPORATING EFFORTS OF CLERGIES, REHABILITATION CENTERS AND JUSTICE SYSTEM

2017 ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Legal System ◽  
Justice System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Numerical Results ◽  
Rehabilitation Centers ◽  
Analytical Results

This study presents a deterministic model for domestic radicalization process in Kenya and uses the model to assess the effect of efforts of good clergies, rehabilitation centers and legal system in lowering radicalization burden. The likelihood of other drivers of radicalization to individuals who are not religious fanatics was considered. The possibility of individuals in rehabilitated subclass quitting back to violent class was considered. The equilibrium points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization computed. The sensitivity analysis of control reproduction number indicates that high intervention rates hold is likely to reduce the radicalization burden. The results indicate that use of good clergies to assist individuals’ radicalized but peaceful, to recover is the best intervention strategy. Estimated numerical results and simulations were carried to confirm analytical results.

scholarly journals Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mouhcine Naim ◽  
Fouad Lahmidi
Keyword(s):  
Epidemic Model ◽  
Deterministic Model ◽  
Sufficient Condition ◽  
Nonlinear Incidence Rate ◽  
Local Asymptotic Stability ◽  
Sis Epidemic Model ◽  
The Stability ◽  
Stochastic Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and pth moment exponential is investigated. Finally, numerical examples are presented.

A Large Rotation Matrix for Nonlinear Framed Structures, Part 2: Numerical Verification

2014 ◽  
Vol 1065-1069 ◽  
pp. 2034-2039
Author(s):  
Jin Duan ◽  
Yun Gui Li
Keyword(s):  
Cantilever Beam ◽  
Numerical Results ◽  
Rotation Matrix ◽  
Numerical Verification ◽  
Structural Stiffness ◽  
Pure Bending ◽  
Large Rotation ◽  
Framed Structures ◽  
Analytical Results ◽  
Good Agreement

In this paper, some numerical verifications would be presented and discussed, mainly including the following three types: (1) the pure bending beam in which the structural stiffness would maintain the original value and not change along with the load; (2) the clamped arc-beam in which the structural stiffness would decrease gradually with the increment of load and the structure would be buckling at some certain load value; and (3) the cantilever beam in which the structural stiffness would increase significantly with the increment of load. For all of the above examples, the present results are in good agreement with the analytical results and numerical results in other literatures, testifying and illustrating the validity of the large rotation matrix for nonlinear framed structure, which is developed in the part 1 of this paper.

Mathematical Modeling and Stability Analysis of Japanese Encephalitis

2020 ◽  
Vol 12 (1) ◽  
pp. 120-127
Author(s):  
Vinod Baniya ◽  
Ram Keval
Keyword(s):  
Mathematical Modeling ◽  
Japanese Encephalitis ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Numerical Verification ◽  
Transmission Potential ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Stability ◽  
Stability Issues

Mathematical modeling of Japanese encephalitis (JE) disease in human population with pig and mosquito has been presented in this paper. The proposed model, which involves three compartments of human (Susceptible, Vaccinated, Infected), two compartments of mosquito (Susceptible, Infected) and three compartments of the pig (Susceptible, Vaccinated, Infected). In this work, it is assumed that JE spreads between susceptible class and infected mosquitoes only. Basic results like boundedness of the model, the existence of equilibrium and local stability issues are investigated. Here, to measure the disease transmission potential in the population the basic reproduction number (R0) from the system has been analyzed w.r.t. control parameters both numerically and theoretically. The dynamical behaviors of the system have been analyzed by using the stability theory of differential equations and numerical simulations at equilibrium points. A numerical verification of results is carried out of the model under consideration.

Linear and Nonlinear Electrical Models of Neurons for Hopfield Neural Network

2016 ◽  
Vol 71 (11) ◽  
pp. 995-1002
Author(s):  
Farah Sarwar ◽  
Shaukat Iqbal ◽  
Muhammad Waqar Hussain
Keyword(s):  
Neural Network ◽  
Neuron Model ◽  
Deterministic Model ◽  
Hopfield Neural Network ◽  
Biological Properties ◽  
Operational Amplifiers ◽  
Nonlinear Input ◽  
Stochastic Neuron ◽  
Output Characteristics ◽  
The Stability

AbstractA novel electrical model of neuron is proposed in this presentation. The suggested neural network model has linear/nonlinear input-output characteristics. This new deterministic model has joint biological properties in excellent agreement with the earlier deterministic neuron model of Hopfield and Tank and to the stochastic neuron model of McCulloch and Pitts. It is an accurate portrayal of differential equation presented by Hopfield and Tank to mimic neurons. Operational amplifiers, resistances, capacitor, and diodes are used to design this system. The presented biological model of neurons remains to be advantageous for simulations. Impulse response is studied and conferred to certify the stability and strength of this innovative model. A simple illustration is mapped to demonstrate the exactness of the intended system. Precisely mapped illustration exhibits 100 % accurate results.

scholarly journals On the Stochastic Dynamics of a Social Epidemics Model

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Xun-Yang Wang ◽  
Peng-Zhan Zhang ◽  
Qing-Shan Yang
Keyword(s):  
Stochastic System ◽  
Stochastic Dynamics ◽  
Deterministic Model ◽  
Random Disturbance ◽  
Disturbance Intensity ◽  
The Stability ◽  
The Individual ◽  
Theoretical Results ◽  
Two Equilibria

Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when R0≤1, we get the estimation between the trajectory of stochastic system and E0=(Π/μs,0,0,0) in the average in time with respect to the disturbance intensity, while when R0>1, stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results.

scholarly journals Stability analysis of a clutch system with uncertain parameters using sparse polynomial chaos expansions

2019 ◽  
Vol 20 (1) ◽  
pp. 104
Author(s):  
Duc Thinh Kieu ◽  
Baptiste Bergeot ◽  
Marie-Laure Gobert ◽  
Sébastien Berger
Keyword(s):  
Stability Analysis ◽  
Polynomial Chaos ◽  
Deterministic Model ◽  
Computational Cost ◽  
Uncertain Parameters ◽  
Sparse Polynomial ◽  
Clutch System ◽  
Frictional Forces ◽  
The Stability ◽  
Polynomial Chaos Expansions

In vehicle transmission systems, frictional forces acting during the sliding phase of the clutch engagement may produce unwanted vibrations. The prediction of the stability of a clutch system remains however a laborious task, as the parameters which have the highest impact on the stability, such as the friction law or the damping, lead to significant dispersions and must be considered as uncertain in such studies. Non-intrusive generalized polynomial chaos (gPC) expansions have already been used in this context. However, the number of deterministic model evaluations (i.e. the computational cost) required to compute the PC coefficients becomes prohibitive for large numbers of uncertain parameters. The sparse polynomial chaos, recently developed by Blatman and Sudret, may overcome this issue. In this paper, the method has been applied to the stability analysis of a clutch system owning up to eight uncertain parameters. Comparisons with the reference Monte Carlo method and classic full PC expansions show that sparse PC expansions allow substantial computational cost reductions while ensuring a high accuracy of the results.

scholarly journals Estimating Friction Parameters in Reaction Wheels for Attitude Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Valdemir Carrara ◽  
Hélio Koiti Kuga
Keyword(s):  
Attitude Control ◽  
Deterministic Model ◽  
High Reliability ◽  
Viscous Friction ◽  
Static Friction ◽  
Friction Model ◽  
Artificial Satellites ◽  
Wide Range ◽  
The Stability ◽  
Friction Parameters

The ever-increasing use of artificial satellites in both the study of terrestrial and space phenomena demands a search for increasingly accurate and reliable pointing systems. It is common nowadays to employ reaction wheels for attitude control that provide wide range of torque magnitude, high reliability, and little power consumption. However, the bearing friction causes the response of wheel to be nonlinear, which may compromise the stability and precision of the control system as a whole. This work presents a characterization of a typical reaction wheel of 0.65 Nms maximum angular momentum storage, in order to estimate their friction parameters. It used a friction model that takes into account the Coulomb friction, viscous friction, and static friction, according to the Stribeck formulation. The parameters were estimated by means of a nonlinear batch least squares procedure, from data raised experimentally. The results have shown wide agreement with the experimental data and were also close to a deterministic model, previously obtained for this wheel. This model was then employed in a Dynamic Model Compensator (DMC) control, which successfully reduced the attitude steady state error of an instrumented one-axis air-bearing table.

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