Global asymptotical stability in a rational difference equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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Global asymptotical stability and sliding bifurcation analysis of a general Filippov-type predator-prey model with a refuge

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126263 ◽

2021 ◽

Vol 405 ◽

pp. 126263

Author(s):

Wenxiu Li ◽

Lihong Huang ◽

Jiafu Wang

Keyword(s):

Bifurcation Analysis ◽

Asymptotical Stability ◽

Global Asymptotical Stability ◽

Predator Prey ◽

Predator Prey Model ◽

Sliding Bifurcation ◽

Prey Model ◽

Filippov Type

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On the rational difference equation $x_{n}=1+\frac{(1-x_{n-k})(1-x_{n-l})(1-x_{n-m})}{x_{n-k}+x_{n-l}+x_{n-m}}$

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-009-0340-8 ◽

2009 ◽

Vol 35 (1-2) ◽

pp. 63-71 ◽

Cited By ~ 1

Author(s):

Maoxin Liao ◽

Xianhua Tang ◽

Changjin Xu

Keyword(s):

Difference Equation ◽

Rational Difference Equation

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Dynamics of a higher-order rational difference equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2005.11.059 ◽

2006 ◽

Vol 178 (2) ◽

pp. 345-354 ◽

Cited By ~ 3

Author(s):

Mehdi Dehghan ◽

Reza Mazrooei-Sebdani

Keyword(s):

Difference Equation ◽

Higher Order ◽

Rational Difference Equation

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Boundedness of solutions and stability of certain second-order difference equation with quadratic term

Advances in Difference Equations ◽

10.1186/s13662-019-2490-9 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Emin Bešo ◽

Senada Kalabušić ◽

Naida Mujić ◽

Esmir Pilav

Keyword(s):

Difference Equation ◽

Initial Conditions ◽

Second Order ◽

Quadratic Term ◽

Real Numbers ◽

Positive Real ◽

Order Difference ◽

Second Order Difference Equation ◽

Order Difference Equation ◽

Rational Difference Equation

AbstractWe consider the second-order rational difference equation $$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$xn+1=γ+δxnxn−12, where γ, δ are positive real numbers and the initial conditions $x_{-1}$x−1 and $x_{0}$x0 are positive real numbers. Boundedness along with global attractivity and Neimark–Sacker bifurcation results are established. Furthermore, we give an asymptotic approximation of the invariant curve near the equilibrium point.

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