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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, ...
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 ...
On the dot product graph of a commutative ring II
(International Electronic Journal of Algebra, 2020)
In 2015, the second-named author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times). We ...
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 ...