[PDF] Top 20 Dynamics of higher order rational difference equation $x_{n+1}=(\alpha+\beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

... the rational difference equation that was investigated by Kulenovic et ...[The Dynamics of x n+1 = A+Bx α+βx n +Cx n n−1 , Facts and ... See full document

... of Equation (1) is locally asymptotically stable when 2 |(be - dc)| <(d + e)(b + ...of Equation (1) is unbounded if a ...of Equation (1) is global ... See full document

... nonlinear difference equations are capable of producing a complicated behavior regardless its ...nonlinear difference equations in proving that every solution of these equations conver to a period two ... See full document

... appropriate difference equation to model a situation? how does one understand the behaviour of the difference equation model once it has been formed? There is no scopes of confusion that the ... See full document

... 0, 1, ...second order difference equations with quadratic terms for which a discrete version of the 16th Hilbert problem does not ...second order difference equations with quadratic terms for which the ... See full document

... this equation is a point that satisfies the condition e x = F ( e x , e x ...x n ∞ n=−k with x n = e x for all n ≥ −k is a solution of that ... See full document

... In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. ... See full document

... years, rational difference equations have attracted the attention of many researchers for varied ...whose dynamics present some new features with respect to the linear ...hand, rational equations ... See full document

... We also state Mawhin’s continuation theorem (see [1]). Let X and Y be two Banach spaces, and L : Dom L ⊂ X → Y is a linear mapping and N : X → Y is a continuous mapping. The mapping L is called a Fredholm ... See full document

... ≠ 1, b ≠ 1 are positive constants, τ: Z ® Z and τ(n + ω) = τ(n), f(n + ω, u) = f(n, u) for any u Î R, ω, m, k Î N where N denotes the set of positive ...the ... See full document

... population dynamics, queuing problems, statistical problems, stochastic time series, combinatorial analysis, number theory, geom- etry, electrical networks, neural networks, quanta in radiation, genetics in ... See full document

... z n − 1 = 0, n = 0, 1,.... (2.1) This equation was considered in [7], where the method of full limiting sequences was used to prove that the equilibrium is globally asymptotically ... See full document

... Rational difference equations that are the ratio of two polynomials are one of the most important and practical classes of nonlinear difference equations. Marwan Aloqeili [] investigated the stability character, ... See full document

... x 1 ) and such n ∈ N for which difference equation ...iteration n + 1 difference equation ...x 1 ) belong to forbidden set F ... See full document

... The global asymptotic behavior of the solutions and oscillation of solution are two such qualitative properties which are very important for applications in many areas such as control theory, mathematical biology, neural ... See full document

... that is, ϕ and ψ are two distinct positive roots of gy 0. From 3.4 we can see that gy 0 does not have two distinct positive roots at all when r ≤ 1, alternatively, 1.3 does not have the nonnegative prime period ... See full document

... In this paper we propose using matrix representation of higher order derivatives. This allows us to find simple expressions for function derivatives and matrix equations deter- mining solution irrespective ... See full document

... fourth- order compact difference scheme with 9 grid points except under certain conditions men- tioned ...convergence order of the CCD2 scheme is less than six for some ...differential equation are ... See full document

... difference equation with constant coefficients, such a formula ...of order greater than or equal to five need not be solved by radicals, which implies that there are linear difference equations with constant ... See full document

... this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et ... See full document