Two‐dimensional solvable system of difference equations with periodic coefficients

2019 ◽  
Vol 42 (18) ◽  
pp. 6757-6774 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equations ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Periodic Coefficients ◽  
Solvable System

scholarly journals ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

2021 ◽  
Vol 21 (1) ◽  
pp. 145-162
Author(s):  
MERVE KARA ◽  
YASIN YAZLIK
Keyword(s):  
Closed Form ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Variable Coefficients ◽  
Linear Difference Equations ◽  
System Of Difference Equations ◽  
Solvable System ◽  
Initial Values ◽  
Non Linear ◽  
Forbidden Set

In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

scholarly journals Permanence for a Generalized Discrete Neural Network System

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stevic
Keyword(s):  
Neural Network ◽  
Difference Equations ◽  
Network System ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Neural Network System ◽  
Nondecreasing Functions

We prove that the system of difference equationsxn+1(i)=λixn(i)+fi(αixn(i+1)−βixn−1(i+1)),i∈{1,2,…,k},n∈ℕ, (we regard thatxn(k+1)=xn(1)) is permanent, provided thatαi≥βi,λi+1∈[0,βi/αi),i∈{1,2,…,k},fi:ℝ→ℝ,i∈{1,2,…,k}, are nondecreasing functions bounded from below and such that there areδi∈(0,1)andM>0such thatfi(αix)≤δix,i∈{1,2,…,k}, for allx≥M. This result considerably extends the results existing in the literature. The above system is an extension of a two-dimensional discrete neural network system.

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