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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 ...
On the periodic logistic equation
(Elsevier, 2006)
We show that the 𝒑-periodic logistic equation 𝒳ₙ₊₁ = μₙ mod 𝒑𝒳ₙ(1 - 𝒳ₙ) has cycles (periodic solutions) of minimal periods 1; 𝒑; 2𝒑; 3𝒑; …. Then we extend Singer’s theorem to periodic difference equations, and use ...
An Extension of Sharkovsy’s Theorem to Periodic Difference Equations
(Elsevier, 2006)
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 ...
Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking
(Taylor & Francis Online, 2009)
The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting ...
The Beverton–Holt model with periodic and conditional harvesting
(Taylor & Francis Online, 2009)
In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton–Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic ...
Periodic Orbits in Periodic Discrete Dynamics
(Elsevier, 2008)
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 ...