Global behavior of \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).

DOI10.1016/S0362-546X(01)00586-7zbMath1042.39523MaRDI QIDQ1875525

S. W. Schultz, Richard DeVault, Gerasimos E. Ladas, Witold A. Kosmala

Publication date: 26 August 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20)

Related Items (72)

The oscillatory character of the recursive sequence \(x_{n+1}= \frac {\alpha+\beta x_{n-k+1}}{A+Bx_{n-2k+1}}\) ⋮ Global attractivity of the recursive sequence \(x_{n+1}= \frac {\alpha- \beta x_{n-k}} {\gamma+ x_n}\) ⋮ On the boundedness character of rational equations, part 3 ⋮ On the recursive sequence \(y_{n+1} = \frac {\alpha+y_{n-1}}{\beta+y_{n}} + \frac {y_{n-1}}{y_{n}}\) ⋮ Dynamic behavior of a recursive sequence ⋮ Asymptotic properties of the positive equilibrium of a discrete survival model ⋮ Global stability and oscillation in nonlinear difference equations of population dynamics ⋮ Unnamed Item ⋮ On the difference equation \(x_{n+1}= \frac{px_{n-s} + x_{n-t}}{qx_{n-s} + x_{n-t}}\) ⋮ On the difference equation \(x_n = \frac{p+x_{n-2}}{qx_{n-t}+x_{n-s}}\) ⋮ On the rational recursive sequence \(x_{n+1}=\frac {\alpha x_n+\beta x_{n-1}+\gamma x_{n-2}+\delta x_{n-3}} {Ax_b+ Bx_{n-1}+ Cx_{n-2}+ Dx_{n-3}}\) ⋮ On the difference equation \(y_{n+1} = \frac {\alpha +\beta e^{-y_n}}{\gamma +y_{n-1}}\) ⋮ Attractivity of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)F(x_{n-1},\dots,x_{n-k})\). ⋮ Global asymptotic stability for a higher order nonlinear rational difference equations ⋮ The characteristics of a higher-order rational difference equation ⋮ Global stability of \(y_{n+1} =\frac {p+qy_{n}+ry_{n-k}}{1+y_{n}}\) ⋮ Open Problems and Conjectures ⋮ Global dynamics for a higher-order rational difference equation ⋮ On the global behavior of a high-order rational difference equation ⋮ On the dynamics of a rational difference equation \(x_{n+1}=\frac{\alpha+\beta x_n+\gamma x_{n-k}}{Bx_n+Cx_{n-k}}\) ⋮ Global asymptotic stability of the higher order equation \(x_{n+1} = \frac{ax_{n}+bx_{n-k}}{A+Bx_{n-k}}\) ⋮ Unnamed Item ⋮ On the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n-k})/g(x_n,x_{n-1},\dots,x_{n-k+1})\) ⋮ Global attractivity in the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1})\) ⋮ Global attractivity in a rational recursive sequence. ⋮ On asymptotic behaviour of the difference equation \(x_{x+1}=\alpha + \frac {x_{n-k}}{x_n}\) ⋮ Dynamics of a higher-order nonlinear difference equation ⋮ Open Problems and Conjectures ⋮ Boundedness and global stability of a higher-order difference equation ⋮ Open Problems and Conjectures ⋮ Global attractivity for a class of higher order nonlinear difference equations. ⋮ On the rational recursive sequence \(x_{n+1}=(A+\sum_{i=0}^{k}\alpha _{i}x_{n - i})/(B+\sum _{i=0}^{k}\beta _{i}x_{n - i})\) ⋮ On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\). ⋮ Unnamed Item ⋮ Global stability of a rational difference equation ⋮ Asymptotic and boundedness behaviour of a rational difference equation ⋮ On the rational recursive sequence \(x_{n+1}=(\alpha - \beta x_{n})/(\gamma - \delta x_{n} - x_{n - k})\) ⋮ Global attractivity of a higher order nonlinear difference equation ⋮ Dynamics of a higher order rational difference equation ⋮ Dynamics of the difference equation \(x_{n+1}=\frac{x_n+p x_{n-k}}{x_n+q}\) ⋮ Dynamics of Kth Order Rational Difference Equation ⋮ Dynamics of a rational difference equation ⋮ On the global attractivity of two nonlinear difference equations ⋮ On the recursive sequence \(x_{n+1}=\frac{x+bx_n}{A+Bx^k_{n-1}}\) ⋮ Boundedness and global attractivity of a higher-order nonlinear difference equation ⋮ Dynamics of a higher order nonlinear rational difference equation ⋮ Dynamics of a rational difference equation ⋮ Global behavior of a higher order nonlinear difference equation ⋮ On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\) ⋮ On the higher order rational recursive sequence \(X_{n} = \frac {A}{X_{n-k}}+\frac {B}{X_{n-3k}}\) ⋮ On the rational difference equation \(y_{n+1}= A+ \frac {y_{n-k}}{y_{n}}\) ⋮ On the difference equation \(y_{n+1}=A + \frac {y_n}{y_{n-k}}\) with \(A < 0\) ⋮ On the rational difference equation \(y_{n+1}=A+\frac {y_n}{y_{n-k}}\) ⋮ On the rational recursive sequence \(x_{n+1}=Ax_{n}+Bx_{n-k}+\frac{\beta x_{n}+\gamma x_{n-k}}{cx_{n}+Dx_{n-k}}\) ⋮ The study of a class of rational difference equations ⋮ Global stability of a higher order rational recursive sequence ⋮ Oscillation and asymptotic behavior of a class of higher order nonlinear recursive sequences ⋮ Dynamics of a non-linear difference equation ⋮ On the recursive sequence \(x_{x+1}= \frac{\alpha+\beta x_{n-k+1}}{A+Bx_{n-k+1}+Cx_{n-2k+1}}\) ⋮ Dynamics of a higher-order rational difference equation ⋮ Global attractors for difference equations dominated by one-dimensional maps ⋮ Global asymptotic behavior of the difference equation \(y_{n+1}=\frac{\alpha \cdot \text{e}^{-(ny_n+(n-k)y_{n-k})}}{\beta +ny_n+(n-k)y_{n-k}}\) ⋮ On the boundedness character of rational equations, part 2 ⋮ On the Recursive Sequencexⁿ⁺¹= ⋮ Global behavior of \(x_{n + 1} = (\alpha + \beta x_{n - k}) /(\gamma + x_n)\) ⋮ On the dynamics of ⋮ Global attractivity of the difference equation \(x_{n+1}=\alpha+(x_{n-k}/x_{n})\) ⋮ On the rational recursive sequence \(x_{n+1}=\frac{\alpha + \beta x_{n-k}}{\gamma-x_{n}}\) ⋮ On the recursive sequence \(x_n=A+x_{n-k}^p/x_{n-1}^r\) ⋮ The qualitative behavior of solutions of a nonlinear difference equation ⋮ Dynamics of a rational difference equation using both theoretical and computational approaches ⋮ On the recursive sequence \(x_{n+1} = \frac {\alpha+\beta x_{n-k+1} +\gamma x_{n-2k+1}}{Bx_{n-k+1} + Cx_{n-2k+1}}\)

This page was built for publication: Global behavior of \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).