Global dynamics of some quadratic difference equations

Mark DiPippo, University of Rhode Island

Abstract

Consider the difference equation^ (n/a)^ where all parameters α, β, ai, bi , aij, bij, i, j = 0,1,..., k and the initial conditions xi, i ∈{– k,..., 0} are nonnegative. We investigate the asymptotic behavior of the solutions of the considered equation. We give simple explicit conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation. We investigate the global dynamics of several anti-competitive systems of rational difference equations which are special cases of general linear fractional system of the form^ (n/a)^ where all parameters and the initial conditions x0, y0 are arbitrary nonnegative numbers such that both denominators are positive. We find the basins of attraction of all attractors of these systems.^ We investigate global dynamics of the equation^ (n/a)^ where the parameters a, c and ƒ are nonnegative numbers with condition a + e + ƒ > 0 and the initial conditions x–1, x0 are arbritary nonnegative numbers such that x–1 + x0 > 0.^

Subject Area

Mathematics

Recommended Citation

Mark DiPippo, "Global dynamics of some quadratic difference equations" (2016). Dissertations and Master's Theses (Campus Access). Paper AAI10141812.
http://digitalcommons.uri.edu/dissertations/AAI10141812

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