scholarly journals Global attractivity in a class of non-autonomous, nonlinear, higher order difference equations

2013 ◽  
Vol 19 (7) ◽  
pp. 1049-1064 ◽  
Author(s):  
H. Sedaghat
Keyword(s):  
Difference Equations ◽  
Global Attractivity ◽  
Higher Order ◽  
Order Difference

scholarly journals On Somek-Dimensional Cyclic Systems of Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Wanping Liu ◽  
Xiaofan Yang ◽  
Bratislav D. Iričanin
Keyword(s):  
Difference Equations ◽  
Global Attractivity ◽  
Transformation Method ◽  
Higher Order ◽  
Order Difference ◽  
Cyclic Systems ◽  
First Time

Motivated by Iričanin and Stević's paper (2006) in which for the first time were considered some cyclic systems of difference equations, here we study the global attractivity of some nonlineark-dimensional cyclic systems of higher-order difference equations. To do this, we use the transformation method from Berenhaut et al. (2007) and Berenhaut and Stević (2007). The main results in this paper also extend our recent results in the work of (Liu and Yang 2010, in press).

scholarly journals Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 108
Author(s):  
Kgatliso Mkhwanazi ◽  
Mensah Folly-Gbetoula
Keyword(s):  
Difference Equations ◽  
Variable Coefficients ◽  
Higher Order ◽  
Order Difference

We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.

TRANSFER EQUIVALENCE AND REALIZATION OF NONLINEAR HIGHER ORDER INPUT/OUTPUT DIFFERENCE EQUATIONS USING MATHEMATICA

1999 ◽  
Vol 09 (01n02) ◽  
pp. 23-35 ◽  
Author(s):  
ÜLLE KOTTA ◽  
MARIS TÕNSO
Keyword(s):  
Control Systems ◽  
Difference Equations ◽  
Space Form ◽  
Higher Order ◽  
Nonlinear Control Systems ◽  
Input Output ◽  
Nonlinear Case ◽  
State Equations ◽  
Order Difference ◽  
Classical State

This paper presents a contribution to the development of symbolic computation tools for discrete-time nonlinear control systems. A set of functions is developed in Mathematica 3.0 that test if the higher order input/output difference equation is realizable in the classical state-space form, and for simple examples, also find such state equations. The approach relies on a new notion of equivalence of higher order difference equations which yields a minimal (i.e. accessible and observable) realization and generalizes the notion of transfer equivalence to the nonlinear case. The application of the developed functions is demonstrated on three examples obtained via identification.

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