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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 ...
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 ...
Folding and unfolding in periodic difference equations
(Elseiver, 2014)
Given a p-periodic difference equation xn+1 = fn mod p(xn), where each fj is a continuous interval map, j = 0, 1, . . . , p − 1, we discuss the notion of folding and unfolding related to this type of non-autonomous equations. ...
The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology
(Taylor & Francis, 2013)
One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then ...
The dynamics of some discrete models with delay under the effect of constant yield harvesting
(Elsevier, 2013)
In this paper, we study the dynamics of population models of the form xn+1 = xnf(xn−1) under the effect of constant yield harvesting. Results concerning stability, boundedness, persistence and oscillations of solutions are ...
The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model
(Wiley, 2017)
In this paper, we study a general discrete–time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation xn+1 = xnf(xn−k) − hxn ...
The Discrete Beverton-Holt Model with Periodic Harvesting in a Periodically Fluctuating Environment
(Springer, 2010)
We investigate the effect of constant and periodic harvesting on the Beverton-Holt model in a periodically fluctuating environment. We show that in a periodically fluctuating environment, periodic harvesting gives a better ...