scholarly journals Nontrivial periodic solutions to delay difference equations via Morse theory

2018 ◽  
Vol 16 (1) ◽  
pp. 885-896 ◽  
Author(s):  
Yuhua Long ◽  
Haiping Shi ◽  
Xiaoqing Deng
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Morse Theory ◽  
Sufficient Conditions ◽  
Asymptotically Linear ◽  
Linear Delay ◽  
Nontrivial Periodic Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

scholarly journals Stability conditions for linear delay difference equations: a survey and perspectives

2015 ◽  
Vol 63 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Jan Čermák
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Stability Conditions ◽  
Linear Delay ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Theoretical Results

Abstract The paper presents an overview of the basic results and methods for stability investigations of higher-order linear autonomous difference equations. The presented criteria formulate several types of necessary and sufficient conditions for the asymptotic stability of the zero solution of studied equations, with a special emphasize put on delay difference equations. Various comments, comparisons, examples and illustrations are given to support theoretical results.

scholarly journals Stability and global attractivity for a class of nonlinear delay difference equations

2005 ◽  
Vol 2005 (3) ◽  
pp. 227-234 ◽  
Author(s):  
Binxiang Dai ◽  
Na Zhang
Keyword(s):  
Difference Equations ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Delay Equation ◽  
Stability Properties ◽  
The Stability ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

A class of nonlinear delay difference equations are considered and some sufficient conditions for global attractivity of solutions of the equation are obtained. It is shown that the stability properties, both local and global, of the equilibrium of the delay equation can be derived from those of an associated nondelay equation.

scholarly journals Dynamics of a Family of Nonlinear Delay Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Qiuli He ◽  
Taixiang Sun ◽  
Hongjian Xi
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We study the global asymptotic stability of the following difference equation:xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…,where0≤k1<k2<⋯<ksand0≤m1<m2<⋯<mtwith{k1,k2,…,ks}⋂‍{m1,m2,…,mt}=∅,the initial values are positive, andf∈C(Es+t,(0,+∞))withE∈{(0,+∞),[0,+∞)}. We give sufficient conditions under which the unique positive equilibriumx-of that equation is globally asymptotically stable.

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