scholarly journals Dynamic Characteristics of Four Systems of Difference Equations with Higher Order

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Abdul Qadeer Khan ◽  
Shahid Mahmood Qureshi ◽  
Imtiaz Ahmed
Keyword(s):  
Fixed Point ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Dynamic Characteristics ◽  
Discrete Systems ◽  
Higher Order ◽  
Dynamical Characteristics ◽  
Globally Stable ◽  
Theoretical Results

In this paper, we explore the global dynamical characteristics, boundedness, and rate of convergence of certain higher-order discrete systems of difference equations. More precisely, it is proved that for all involved respective parameters, discrete systems have a trivial fixed point. We have studied local and global dynamical characteristics at trivial fixed point and proved that trivial fixed point of the discrete systems is globally stable under respective definite parametric conditions. We have also studied boundedness and rate of convergence for under consideration discrete systems. Finally, theoretical results are confirmed numerically. Our findings in this paper are considerably extended and improve existing results in the literature.

scholarly journals Global Dynamical Properties of Rational Higher-Order System of Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
A. Q. Khan ◽  
S. M. Qureshi
Keyword(s):  
Numerical Simulation ◽  
Positive Solution ◽  
Higher Order ◽  
Order System ◽  
Discrete Time System ◽  
System Of Difference Equations ◽  
Time System ◽  
Dynamical Properties ◽  
Globally Stable ◽  
Theoretical Results

In this paper, global dynamical properties of rational higher-order system are explored in the interior of ℝ+3. It is explored that under certain parametric conditions, the discrete-time system has at most eight equilibria. By the method of linearization, local dynamics has been explored. It is explored that positive solution of the system is bounded, and moreover fixed point P000 is globally stable if α1/α2<1, α4/α5<1, α7/α8<1. It is also investigated that the positive solution of the system under consideration converges to P000. Lastly, theoretical results are confirmed by numerical simulation. The presented work is significantly extended and improves current results in the literature.

scholarly journals Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

2021 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn&minus;m^2, yn+1=A+Bxn/xn&minus;m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

scholarly journals Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190376
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Difference Equations ◽  
Arbitrary Order ◽  
Theme Issue ◽  
Topological Methods ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Theoretical Results

Motivated by the study of systems of higher-order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral equations, where the nonlinearities and the functionals involved depend on some derivatives. We improve and complement earlier results in the literature. We also provide some examples in order to illustrate the applicability of the theoretical results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

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}&sup2;)) with A,B and initial conditions are positive numbers, and m&isin;{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}&sup2;)) 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 Dynamics of System of Higher Order Difference Equations with Quadratic Terms

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}&sup2;)),y_{n+1}=A+B((x_{n})/(x_{n-m}&sup2;)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

scholarly journals On New Quicker N-Tupled Xed Point Implicit Iterations for Contractive-Like Mappings and Comparison of their Rate of Convergence in Hyperbolic Metric Spaces

2019 ◽  
Author(s):  
Ahmed H. Soliman ◽  
Mohamed A. Barakat ◽  
M. Imdad ◽  
Tamer Nabil
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Rate Of Convergence ◽  
Metric Spaces ◽  
Iteration Process ◽  
Hyperbolic Metric ◽  
Iteration Processes ◽  
Implicit Iteration ◽  
Theoretical Results

In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

Sign in / Sign up

Export Citation Format

Share Document