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.

CHAOTIC SECURE COMMUNICATION BASED ON THE CONCEPT OF EQUIVALENT CONTROL

2006 ◽  
Vol 16 (02) ◽  
pp. 419-425 ◽  
Author(s):  
MAO-YIN CHEN ◽  
DONG-HUA ZHOU ◽  
YUN SHANG
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Secure Communication ◽  
Sliding Mode ◽  
Higher Order ◽  
Order System ◽  
Augmented System ◽  
Response System ◽  
Equivalent Control ◽  
Chaotic Secure Communication

This Letter considers the problem of chaotic secure communication in the drive-response framework. The drive system can be augmented into a higher order system, and then a sliding mode observer based response system can be constructed to synchronize this augmented system. If they satisfy certain conditions, the hidden message can be recovered directly by the concept of equivalent control. Theoretical analysis and numerical simulation verify the effectiveness of the proposed method.

scholarly journals Dynamics of a Higher-Order System of Difference Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Qi Wang ◽  
Qinqin Zhang ◽  
Qirui Li
Keyword(s):  
Positive Integer ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Order System ◽  
Real Numbers ◽  
Precise Description ◽  
System Of Difference Equations ◽  
Positive Real

Consider the following system of difference equations:xn+1(i)=xn-m+1(i)/Ai∏j=0m-1xn-j(i+j+1)+αi,xn+1(i+m)=xn+1(i),x1-l(i+l)=ai,l,Ai+m=Ai,αi+m=αi,i,l=1,2,…,m;n=0,1,2,…,wheremis a positive integer,Ai,αi,i=1,2,…,m, and the initial conditionsai,l,i,l=1,2,…,m,are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results.

scholarly journals Global Dynamics of a 3 × 6 System of Difference Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
S. M. Qureshi ◽  
A. Q. Khan
Keyword(s):  
Difference Equations ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
System Of Difference Equations ◽  
Globally Asymptotically Stable ◽  
Rational Difference Equations ◽  
Dynamical Properties ◽  
Theoretical Results

In the proposed work, global dynamics of a 3×6 system of rational difference equations has been studied in the interior of R+3. It is proved that system has at least one and at most seven boundary equilibria and a unique +ve equilibrium under certain parametric conditions. By utilizing method of Linearization, local dynamical properties about equilibria have been investigated. It is shown that every +ve solution of the system is bounded, and equilibrium P0 becomes a globally asymptotically stable if α1<α2,α4<α5, α7<α8. It is also shown that every +ve solution of the system converges to P0. Finally theoretical results are verified numerically.

scholarly journals On a higher-order system of difference equations

2013 ◽  
pp. 1-18 ◽  
Author(s):  
Stevo Stevic ◽  
Mohammed Ali Alghamdi ◽  
Abdullah Alotaibi ◽  
Naseer Shahzad
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Order System ◽  
System Of Difference Equations

scholarly journals Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Changjin Xu
Keyword(s):  
Discrete Time ◽  
System Modelling ◽  
Discrete Time System ◽  
Time System ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Time Systems ◽  
The Given ◽  
Theoretical Results

A class of discrete-time system modelling a network with two neurons is considered. First, we investigate the global stability of the given system. Next, we study the local stability by techniques developed by Kuznetsov to discrete-time systems. It is found that Neimark-Sacker bifurcation (or Hopf bifurcation for map) will occur when the bifurcation parameter exceeds a critical value. A formula determining the direction and stability of Neimark-Sacker bifurcation by applying normal form theory and center manifold theorem is given. Finally, some numerical simulations for justifying the theoretical results are also provided.

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 On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description

2015 ◽  
Vol 63 (2) ◽  
pp. 423-433 ◽  
Author(s):  
P. Ostalczyk
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Discrete Time System ◽  
Input Matrix ◽  
Time System ◽  
Discrete State ◽  
System Description ◽  
Numerical Examples ◽  
Discrete State Space ◽  
Space Description

Abstract In this paper three simplified forms of the fractional-order (FO) backward difference (BD) are proposed and analysed. Due to time and frequency characteristics criteria parameters of simplified forms of the FOBDs are chosen. Applications of the simplified forms of the FOBDs diminish a number of multiplications and additions needed to evaluate the FOBD. This is very important in real-time microprocessor calculations. It is proved that in a discrete state-space description of a fractional-order system one should correct the input matrix with simplified forms of the FOBD. Investigations are supported by two numerical examples

A New Method for Discrete-Time System Reduction

1988 ◽  
Author(s):  
Ioannis S. Apostolakis ◽  
John Diamessis ◽  
David Jordan
Keyword(s):  
Discrete Time ◽  
New Method ◽  
Discrete Time System ◽  
Time System ◽  
System Reduction
Sign in / Sign up

Export Citation Format

Share Document