Global attractivity in nicholson's blowflies

Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

“…Since this equation explains Nicholson's data of blow®ies more accurately (see [15]), it is now referred to as the Nicholson's blow°ies equation and has been studied by many researchers (see [11,17,18] and the references cited therein). Notice that after rescaling with Dirichlet boundary conditions has been proposed and investigated by So and Yang [19].…”

Existence and Exponential Convergence of almost Periodic Solutions for a Discrete Nicholson’s Blowflies Model with Nonlinear Harvesting Term

“…3.As Nicholson's model under consideration is involving a nonlinear harvesting term, one can easily figure out that some of the results reported in the literature might be no longer applicable for proving the existence and exponential convergence of almost periodic solutions of (4). This implies that the main theorems of this paper improve as well as extend some of previously obtained results among them we list for instance [4,9,10,23]. 4.The results of this paper could be generalized to Nicholson's model with patch structure and nonlinear harvesting terms.…”

“…Further, assume x * (n) is positive almost periodic solution of (4) in the set B * . Then, the solution x(n, n 0 , ϕ) of (4) with ϕ ∈ C 0 converges exponentially to x * (n) as n → ∞.…”

“…The dynamical behavior of solutions for various modifications of this model and its discrete analogue has been extensively studied by many authors during the last couple of decades. For the background of model (1), we suggest the reader to consult some relevant papers [3,4,5,6,7,8,9,10,11]. It is well-known that the optimal management of renewable resources has direct relationship to sustainable development of population.…”

“…We shall employ the contraction mapping principle to establish sufficient conditions for the existence of an almost periodic solution for (4). By constructing an appropriate Lyapunov functional, we also prove that the solutions of (4) converge exponentially to an almost periodic solution.…”