Stability analysis of a deterministic model of Zika/Dengue co-circulation

2019 ◽  
Vol 12 (04) ◽  
pp. 1950045 ◽  
Author(s):  
Mike Binder ◽  
Sergei S. Pilyugin
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Human Population ◽  
Deterministic Model ◽  
Sir Model ◽  
System Of Differential Equations ◽  
Dengue Viruses ◽  
Si Model ◽  
The Stability

We consider a deterministic model of Zika and Dengue viruses co-circulating in a human population. We study the system of differential equations modeling the dynamics of the diseases that can either be transmitted directly (host-to-host) or indirectly (host-vector-host). We use an SIR model for hosts and an SI model for vectors in the homogeneous populations. The stability of the model has been analyzed both qualitatively and quantitatively.

scholarly journals Some remarks on the stability analysis in Robe's three body problem

1982 ◽  
Vol 5 (1) ◽  
pp. 195-202
Author(s):  
R. Meire
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Body Problem ◽  
Computer Time ◽  
System Of Differential Equations ◽  
Three Body Problem ◽  
The Stability ◽  
Three Body ◽  
Improved Technique ◽  
Transition Curves

An improved technique is presented for the stability analysis of Robe's3-body problem which gives more accurate results for the transition curves in the parameter plane than does Robe's paper.A novel property of the system of differential equations describing the motion is used, which reduces the computer time by more than50%.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

The Analysis of the Systems Stability of Linear Differential Equations Based on the Transformation of Difference Schemes

2019 ◽  
Vol 20 (9) ◽  
pp. 542-549 ◽  
Author(s):  
S. G. Bulanov
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computer Analysis ◽  
Linear Differential Equations ◽  
System Stability ◽  
The Difference ◽  
Linear Differential ◽  
The Stability

The approach to the analysis of Lyapunov systems stability of linear ordinary differential equations based on multiplicative transformations of difference schemes of numerical integration is presented. As a result of transformations, the stability criteria in the form of necessary and sufficient conditions are formed. The criteria are invariant with respect to the right side of the system and do not require its transformation with respect to the difference scheme, the length of the gap and the step of the solution. A distinctive feature of the criteria is that they do not use the methods of the qualitative theory of differential equations. In particular, for the case of systems with a constant matrix of the coefficients it is not necessary to construct a characteristic polynomial and estimate the values of the characteristic numbers. When analyzing the system stability with variable matrix coefficients, it is not necessary to calculate the characteristic indicators. The varieties of criteria in an additive form are obtained, the stability analysis based on them being equivalent to the stability assessment based on the criteria in a multiplicative form. Under the conditions of a linear system stability (asymptotic stability) of differential equations, the criteria of the systems stability (asymptotic stability) of linear differential equations with a nonlinear additive are obtained. For the systems of nonlinear ordinary differential equations the scheme of stability analysis based on linearization is presented, which is directly related to the solution under study. The scheme is constructed under the assumption that the solution stability of the system of a general form is equivalent to the stability of the linearized system in a sufficiently small neighborhood of the perturbation of the initial data. The matrix form of the criteria allows implementing them in the form of a cyclic program. The computer analysis is performed in real time and allows coming to an unambiguous conclusion about the nature of the system stability under study. On the basis of a numerical experiment, the acceptable range of the step variation of the difference method and the interval length of the difference solution within the boundaries of the reliability of the stability analysis is established. The approach based on the computer analysis of the systems stability of linear differential equations is rendered. Computer testing has shown the feasibility of using this approach in practice.

scholarly journals Influence of rate of resource flow on dynamics of community of people and artificial beings

2021 ◽  
Vol 16 (4) ◽  
pp. 0
Author(s):  
Vladimir Kotov
Keyword(s):  
Differential Equations ◽  
Human Population ◽  
Well Being ◽  
Reproduction Rate ◽  
System Of Differential Equations ◽  
Equilibrium Solutions ◽  
Resource Flow ◽  
Population Sizes ◽  
Decreasing Functions ◽  
Function Constant

We develop and analyze a population model allowing us to examine a system, where people coexist with artificial beings (robots) and the both consume the same resource entering the system. The robot population consists of friendly and aggressive robots that differ in their attitudes towards people. We propose a system of differential equations, which define a dynamics of the populations of people, friendly robots and aggressive robots, and discuss different scenarios of the system evolution including those that lead to disappearance of the human population. We determine conditions that ensure a more or less prosperous future for humanity. We analyze the behavior of the system for different time dependences of the rate of the resource flow (a constant function, a step-like function, constant functions with undershoots and overshoots, a periodic function, monotonically increasing and decreasing functions). Our analysis shows that the dynamics of the rate of the resource flow defines the changes of the tendencies of the population sizes. Among the obtained solutions, there are solutions that lead to an equilibrium between populations. For people this equilibrium may be regarded as favorable if robots prefer to benefit from communication with people, but not from their extermination. However, equilibrium solutions imply a constant or slowly changes of the rate of the resource flow. Short-term changes of the rate of the resource flow modify the balance between the human population and the robot population. Accumulation of the changes can even lead to disappearance of one of the populations. Qualitative analyzes of the proposed system of differential equations along with computer simulations allow us to conclude that there are some necessary conditions for a well-being of the humans and robots. These conditions are as follows. Firstly, the benefit of the robot from communicating with people has to be higher than the benefit from their extermination. Secondly, to prevent the appearance of the aggressive robots the humanity has to regulate effectively the size of its own population. Thirdly, people have to be able to restrict their needs while maintaining the reproduction rate.

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.

Precise Stability Analysis of Stepped Telescopic Booms and Practical Algorithm

2013 ◽  
Vol 395-396 ◽  
pp. 871-876
Author(s):  
Liang Du ◽  
Peng Lan ◽  
Nian Li Lu
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Energy Method ◽  
Cross Sectional ◽  
Component Method ◽  
Practical Algorithm ◽  
The Stability ◽  
Precise Expression ◽  
Constant Section

To analyze the stability of stepped telescopic booms accurately, using vertical and horizontal bending theory, this paper established the deflection differential equations of stepped column model of arbitrary sectioned telescopic boom, the stability were analyzed, and obtained the precise expression of the buckling characteristic equation; Took certain seven-sectioned telescopic booms as example, by comparing the results with ANSYS, the accuracy of the equations deduced in this paper was verified. Presented the equivalent component method for the stability analysis of multi-stepped column, the equivalent cross-sectional moment of inertia was deduced by energy method, thus the stability of stepped column equivalent to that of constant section component. By comparing the results with exact value, the precision of equivalent component method was verified which was convenient for stability analysis of telescopic boom.

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