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The effect of maps permutation on the global attractor of a periodic Beverton-Holt model
(Elsevier, 2020-04-01)
Consider a p-periodic difference equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps affect the global attractor? In this paper, we limit this general question ...
Stability and bifurcation analysis of a discrete-time predator-prey model with strong Allee effect
(Taylor & Francis, 2020-03-16)
In this paper, we investigate the impact of Allee effect on the stability of a discrete-time predator-prey model with a non-monotonic functional response. The proposed model supports the coexistence of two steady states, ...
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 ...
Basin of Attraction through Invariant Curves and Dominant Functions
(Hindawi, 2015)
We study a second-order difference equation of the form 𝑧ₙ₊₁= 𝑧ₙ𝐹(𝑧ₙ₋₁) + ℎ, where both 𝐹(𝑧) and 𝑧𝐹(𝑧) are decreasing. We consider a set of invariant curves at ℎ = 1 and use it to characterize the behaviour of ...
Harvesting and stocking in discrete-time contest competition models with open problems and conjectures
(Palestine Polytechnic University, 2016)
In this survey, we present a class of first and second-order difference equations representing general form of discrete models arising from single-species with contest competition. Then, we consider various harvesting/stocking ...
Advances in periodic difference equations with open problems
(Springer, 2014)
In this paper, we review some recent results on the dynamics of semi-dynamical systems generated by the iteration of a periodic sequence of continuous maps. In particular, we state several open problems focused on the ...
A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking
(Hindawi, 2013)
We consider discrete models of the form 𝒳ₙ₊₁= 𝒳ₙ𝒇(𝒳ₙ₋₁) + 𝒉ₙ , where 𝒉ₙ is a nonnegative 𝒑-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the ...
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 ...
A new characterization of periodic oscillations in periodic difference equations
(Elsevier, 2011-11)
In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the ...
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 ...