scholarly journals The Stability Cone for a Matrix Delay Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
M. M. Kipnis ◽  
V. V. Malygina
Keyword(s):  
Difference Equation ◽  
Asymptotically Stable ◽  
Delay Difference Equation ◽  
The Matrix ◽  
The Stability ◽  
Delay Difference

We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation . We assume that and are simultaneously triangularizable matrices. We construct points in which are functions of eigenvalues of matrices ,   such that the equation is asymptotically stable if and only if all the points lie inside the stability cone.

scholarly journals Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
G. M. Moremedi ◽  
I. P. Stavroulakis
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Real Numbers ◽  
First Order ◽  
All Solutions ◽  
Delay Difference ◽  
Constant Argument

Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0,  n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0,  n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

Sign in / Sign up

Export Citation Format

Share Document