The Dynamics and Attractivity for a Rational Recursive Sequence of Order Three

This paper is concerned with the behavior of solution of the nonlinear difference equation where the initial conditions are arbitrary positive real numbers and a,b,c,d,e are positive constants

On a generalized cyclic-type system of difference equations with maximum

In this paper we investigate the behaviour of the solutions of the following k-dimensional cyclic system of difference equations with maximum: xi(n + 1) = max ( Ai x p i (n) x q i+1 (n − 1) , i = 1, 2, . . . , k − 1, xk (n + 1) = max ( Ak x p k (n) x q 1 (n − 1) where n = 0, 1, . . . , Ai > 1, for i = 1, 2, . . . , k, whereas the exponents p, q and the initial values xi(−1), xi(0), i = 1, 2, . . . , k are positive real numbers

Study of a cyclic system of difference equations with maximum

In this paper we study the behaviour of the solutions of the following cyclic system of difference equations with maximum: xi(n + 1) = max � Ai xi(n) xi+1(n − 1) , i = 1, 2, . . . , k − 1, xk (n + 1) = max � Ak xk (n) x1(n − 1) where n = 0, 1, 2, . . . , Ai , i = 1, 2, . . . , k, are positive constants, xi(−1), xi(0), i = 1, 2, . . . , k, are real positive numbers. Finally for k = 2 under some conditions we find solutions which converge to periodic six solutions

Study of a system of difference equations with maximum

In this paper we study the behaviour of the solutions of the following cyclic system of difference equations with maximum: $$\begin{split} x_i(n+1)&=\max\left\{A_i,\displaystyle{\frac{x_i(n)}{x_{i+1}(n-1)}}\right\},\qquad i=1,2,\dots,k-1,\\ x_k(n+1)&=\max\left\{A_k,\displaystyle{\frac{x_k(n)}{x_1(n-1)}}\right\} \end{split}$$ where $n=0,1,2,\dots$, $A_i$, $i=1,2,\dots,k,$ are positive constants, $x_i(-1), x_i(0)$, $i=1,2,\dots,k,$ are real positive numbers. Finally for $k=2$ under some conditions we find solutions which converge to periodic six solutions

On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by y n p ry n−s / q φ n y n−1 , y n−2 , . . . , y n−m y n−s , n ∈ N 0 , with p ≥ 0, r, q > 0, s, m ∈ N and positive initial values, and present some sufficient conditions for the parameters and maps φ n : R m → R , n ∈ N 0 , under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al

On the Max-Type Equation +1=max{1/,−1} with a Period-Two Parameter

We study the behavior of the well-defined solutions of the max type difference equation +1=max{1/,−1}, =0,1,…, where the initial conditions are arbitrary nonzero real numbers and {} is a period-two sequence of real numbers with ∈[0,∞)