scholarly journals Global Dynamics of Sixth-Order Fuzzy Difference Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Abdul Khaliq ◽  
Muhammad Adnan ◽  
Abdul Qadeer Khan
Keyword(s):  
Difference Equation ◽  
Equilibrium Point ◽  
Difference Equations ◽  
Numerical Solutions ◽  
Nonnegative Solution ◽  
Real Life ◽  
Characterization Theorem ◽  
Sixth Order ◽  
Global Dynamics ◽  
Life Problems

Across many fields, such as engineering, ecology, and social science, fuzzy differences are becoming more widely used; there is a wide variety of applications for difference equations in real-life problems. Our study shows that the fuzzy difference equation of sixth order has a nonnegative solution, an equilibrium point and asymptotic behavior. y i + 1 = D y i − 1 y i − 2 / E + F y i − 3 + G y i − 4 + H y i − 5 , i = 0,1,2 , … , where y i is the sequence of fuzzy numbers and the parameter D , E , F , G , H and the initial condition y − 5 , y − 4 , y − 3 , y − 2 , y − 1 , y 0 are nonnegative fuzzy number. The characterization theorem is used to convert each single fuzzy difference equation into a set of two crisp difference equations in a fuzzy environment. So, a pair of crisp difference equations is formed by converting the difference equation. The stability of the equilibrium point of a fuzzy system has been evaluated. By using variational iteration techniques and inequality skills as well as a theory of comparison for fuzzy difference equations, we investigated the governing equation dynamics, such as its boundedness, existence, and local and global stability analysis. In addition, we provide some numerical solutions for the equation describing the system to verify our results.

scholarly journals Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Mohamed S. Mohamed ◽  
Khaled A. Gepreel ◽  
Faisal A. Al-Malki ◽  
Nouf Altalhi
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Numerical Solutions ◽  
Optimal Parameter ◽  
Transformation Method ◽  
Series Solutions ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Physical Problems ◽  
Differential Difference Equation

A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method.

scholarly journals Global Dynamics of a Higher Order Difference Equation with a Quadratic Term

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Difference Equation ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Quadratic Term ◽  
Global Dynamics ◽  
Order Difference ◽  
Convergence Of Solutions ◽  
Order Difference Equation

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers, and m∈{2,3,⋯}. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.

scholarly journals Global Dynamics of a Higher Order Difference Equation with Quadratic Term

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Difference Equation ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Quadratic Term ◽  
Global Dynamics ◽  
Order Difference ◽  
Order Difference Equation ◽  
Global Asymptotically Stability

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers. Especially we study the boundedness, periodicity, global asymptotically stability and rate of convergence of related higher order difference equations.

scholarly journals Multiple Attractors for a Competitive System of Rational Difference Equations in the Plane

2011 ◽  
Vol 2011 ◽  
pp. 1-35 ◽  
Author(s):  
S. Kalabušić ◽  
M. R. S. Kulenović ◽  
E. Pilav
Keyword(s):  
Equilibrium Point ◽  
Difference Equations ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Global Dynamics ◽  
Competitive System ◽  
Multiple Attractors ◽  
Rational Difference Equations ◽  
Globally Attractive

We investigate global dynamics of the following systems of difference equationsxn+1=β1xn/(B1xn+yn),yn+1=(α2+γ2yn)/(A2+xn),n=0,1,2,…, where the parametersβ1,B1,β2,α2,γ2,A2are positive numbers, and initial conditionsx0andy0are arbitrary nonnegative numbers such thatx0+y0>0. We show that this system has up to three equilibrium points with various dynamics which depends on the part of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points or nonhyperbolic equilibrium points are separated by the global stable manifolds of either saddle points or of nonhyperbolic equilibrium points. We give an example of globally attractive nonhyperbolic equilibrium point and semistable non-hyperbolic equilibrium point.

The Psychologist in the Medical School: An Example of Solving Real-Life Problems

1970 ◽  
Author(s):  
Matisyohu Weisenberg ◽  
Carl Eisdorfer ◽  
C. Richard Fletcher ◽  
Murray Wexler
Keyword(s):  
Medical School ◽  
Real Life ◽  
Life Problems

scholarly journals AnANN Model Trained on Regional Data in the Prediction of Particular Weather Conditions

2021 ◽  
Vol 11 (11) ◽  
pp. 4757
Author(s):  
Aleksandra Bączkiewicz ◽  
Jarosław Wątróbski ◽  
Wojciech Sałabun ◽  
Joanna Kołodziejczyk
Keyword(s):  
Atmospheric Pressure ◽  
Real Life ◽  
Real Data ◽  
Weather Conditions ◽  
Maximum Temperature ◽  
Air Masses ◽  
Weather Forecasts ◽  
Life Problems ◽  
The World ◽  
The City

Artificial Neural Networks (ANNs) have proven to be a powerful tool for solving a wide variety of real-life problems. The possibility of using them for forecasting phenomena occurring in nature, especially weather indicators, has been widely discussed. However, the various areas of the world differ in terms of their difficulty and ability in preparing accurate weather forecasts. Poland lies in a zone with a moderate transition climate, which is characterized by seasonality and the inflow of many types of air masses from different directions, which, combined with the compound terrain, causes climate variability and makes it difficult to accurately predict the weather. For this reason, it is necessary to adapt the model to the prediction of weather conditions and verify its effectiveness on real data. The principal aim of this study is to present the use of a regressive model based on a unidirectional multilayer neural network, also called a Multilayer Perceptron (MLP), to predict selected weather indicators for the city of Szczecin in Poland. The forecast of the model we implemented was effective in determining the daily parameters at 96% compliance with the actual measurements for the prediction of the minimum and maximum temperature for the next day and 83.27% for the prediction of atmospheric pressure.

scholarly journals Formulating Modes of Cooperative Leaning for Education for Sustainable Development

2021 ◽  
Vol 13 (6) ◽  
pp. 3465
Author(s):  
Jordi Colomer ◽  
Dolors Cañabate ◽  
Brigita Stanikūnienė ◽  
Remigijus Bubnys
Keyword(s):  
Sustainable Development ◽  
Real Life ◽  
Education For Sustainable Development ◽  
Professional Life ◽  
Global Challenges ◽  
Life Problems ◽  
The Face ◽  
Contemporary Education ◽  
The Impact

In the face of today’s global challenges, the practice and theory of contemporary education inevitably focuses on developing the competences that help individuals to find meaningfulness in their societal and professional life, to understand the impact of local actions on global processes and to enable them to solve real-life problems [...]

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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