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- W2783149910 abstract "We investigate the global asymptotic stability of the solutions of begin{document}$X_{n+1}=frac{β X_{n-l} + γ X_{n-k}}{A + X_{n-k}} $end{document} for begin{document}$n=1,2, ...$end{document} , where begin{document}$l$end{document} and begin{document}$k$end{document} are positive integers such that begin{document}$l≠ k$end{document} . The parameters are positive real numbers and the initial conditions are arbitrary nonnegative real numbers. We find necessary and sufficient conditions for the global asymptotic stability of the zero equilibrium. We also investigate the positive equilibrium and find the regions of parameters where the positive equilibrium is a global attractor of all positive solutions. Of particular interest for this generalized equation would be the existence of unbounded solutions and the existence of prime period two solutions depending on the combination of delay terms ( begin{document}$l$end{document} , begin{document}$k$end{document} ) being (odd, odd), (odd, even), (even, odd) or (even, even). In this manuscript we will investigate these aspects of the solutions for all such combinations of delay terms." @default.
- W2783149910 created "2018-01-26" @default.
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- W2783149910 date "2018-01-01" @default.
- W2783149910 modified "2023-09-26" @default.
- W2783149910 title "On the asymptotic character of a generalized rational difference equation" @default.
- W2783149910 doi "https://doi.org/10.3934/dcds.2018070" @default.
- W2783149910 hasPublicationYear "2018" @default.
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