Department of Mathematics and Statistics
Work by the faculty and students of the Department of Mathematics and Statistics
Recent Submissions
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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 ... -
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, ... -
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 ... -
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 ... -
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 ... -
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. ... -
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 ... -
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 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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
Martingale problem for superprocesses with non-classical branching functional
(Elsevier, 2006)The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of ...
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