Topic
Rational difference equation
About: Rational difference equation is a research topic. Over the lifetime, 279 publications have been published within this topic receiving 6469 citations.
Papers published on a yearly basis
Papers
Book•
31 May 1993
TL;DR: The Riccati Difference Equation as discussed by the authors is a generalization of the generalized contraction principle for nonlinear difference equations. But it is not suitable for systems of nonlinear change equations.
Abstract: Preface. 1. Introduction and Preliminaries. 2. Global Stability Results. 3. Rational Recursive Sequences. 4. Applications. 5. Periodic Cycles. 6. Open Problems and Conjectures. Appendix: A. The Riccati Difference Equation. B. A Generalized Contraction Principle. C. Global Behaviour of Systems of Nonlinear Difference Equations. Bibliography. Subject Index. Author Index.
1,308 citations
TL;DR: In this article, the authors investigated the global stability, the periodic character and the boundedness nature of solutions of the equation in the title for all admissible nonnegative values of the parameters and the initial conditions.
Abstract: We investigate the global stability, the periodic character and the boundedness nature of solutions of the equation in the title for all admissible nonnegative values of the parameters and the initial conditions. We show that the solutions exhibit a trichotomy character depending on how the parameter γ compares to the sum of the parameters δ and A.
384 citations
TL;DR: In this article, the authors give a short proof of the Cushing-Henson conjecture concerning the Beverton-Holt difference equation, and show that a periodic environment is always deleterious for populations modeled by this equation.
Abstract: We give a short proof of the Cushing-Henson conjecture
concerning Beverton-Holt difference equation, which is important in theoretical
ecology. The main result shows that a periodic environment is
always deleterious for populations modeled by the Beverton-Holt difference
equation.
119 citations
TL;DR: The stability properties and semi-cycle behavior of the solution of the difference equation x n + 1 = x n - 1 a - xn - 1 x n , n = 0, 1, 2, … , is investigated.
116 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 7 |
| 2020 | 11 |
| 2019 | 10 |
| 2018 | 10 |
| 2017 | 9 |
| 2016 | 14 |