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Existence and stability of periodic orbits of periodic difference equations with delays
(World Scientific Publishing, 2008)
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic ...
An Extension of Sharkovsy’s Theorem to Periodic Difference Equations
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric ...
Periodic Orbits in Periodic Discrete Dynamics
We study the combinatorial structure of periodic orbits of nonautonomous difference equations 𝒳ₙ₊₁ = 𝒇ₙ(𝒳ₙ) in a periodically fluctuating environment. We define the Ӷ-set to be the set of minimal periods that are not ...