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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...