Global Attractivity of a Higher-Order Difference Equation by R. Abo-Zeid

“…The aim of this work is to investigate the global stability, periodic nature, oscillation, and the boundedness of all admissible solutions of the difference equation xn+1=Axn-2r-1/(B-C∏i=lkxn-2i), n=0,1,2,… where A,B,C are positive real numbers and l,r,k are nonnegative integers, such that l≤k.…”
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Divergent sequences satisfying the linear fractional transformations by A. McD. Mercer

“…A real sequence {xn}1∞ which satisfies the recurrence xn+1=axn+bcxn+d, in which all of a,b,c,d are real will, for certain values of these constants, be divergent. …”
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Qualitative Behavior of Rational Difference Equation of Big Order by M. M. El-Dessoky

“…We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequence xn+1=axn-l+bxn-x/c+dxn-lxn-k, n=0,1,…, where the parameters a,  b,  c, and d are positive real numbers, and the initial conditions x-t,x-t+1,…,x-1 and x0 are positive real numbers where t=maxk,l.…”
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The Stability Cone for a Matrix Delay Difference Equation by M. M. Kipnis, V. V. Malygina

“…We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation 𝑥𝑛=𝐴𝑥𝑛−1+𝐵𝑥𝑛−𝑘. We assume that 𝐴 and 𝐵 are 𝑚×𝑚 simultaneously triangularizable matrices. …”
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Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques by M. Khalid Mahmood, Farooq Ahmad

“…For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the form axn≡b(mod pk), k≥1, where a,b, and n>0 are integers which are not divisible by an odd prime p. …”
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On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation by Qianhong Zhang, Fubiao Lin

“…The aim of this paper is to investigate the dynamical behavior of the following model which describes the logistic difference equation taking into account the subjectivity in the state variables and in the parameters. xn+1=Axn(1~-xn),  n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers. …”
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The Neimark–Sacker Bifurcation and Global Stability of Perturbation of Sigmoid Beverton–Holt Difference Equation by M. R. S. Kulenović, Connor O’Loughlin, E. Pilav

“…We present the bifurcation results for the difference equation xn+1=xn2/axn2+xn−12+f where a and f are positive numbers and the initial conditions x−1 and x0 are nonnegative numbers. …”
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Asymptotic Stability for a Class of Nonlinear Difference Equations by Chang-you Wang, Shu Wang, Zhi-wei Wang, Fei Gong, Rui-fang Wang

“…We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max⁡⁡{l,k,s,t} and α,a,b,c are positive constants. …”
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