Abstract
In this paper, we consider nonlinear density-dependent mortality Nicholson’s blowflies system involving patch structures and asymptotically almost periodic environments. By developing an approach based on differential inequality techniques coupled with the Lyapunov function method, some criteria are demonstrated to guarantee the global attractivity of the addressed systems. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the obtain results.
Highlights
IntroductionThe following nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure:
The following nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure:n xi(t) = –aii(t) + bii(t)e–xi(t) +aij(t) – bij(t)e–xj(t) j=1,j=i m+ βij(t)xi t – τij(t) e–γij(t)xi(t–τij(t)), j=1 i ∈ Q := {1, 2, . . . , n}, (1.1)has been used in [1, 2] to describe the dynamics of recruitment-delayed model with the Rickers-type birth function and the harvesting strategy Type II
Inspired by the above analysis, in this paper, under the weaker assumptions (1.7)–(1.10), we develop a novel approach to demonstrate the global stability of positive asymptotically almost-periodic solutions for system (1.1)
Summary
The following nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure:. Aii(t) – bii(t)e–xi(t) is a nonlinear density-dependent mortality term which represents the death rate of the current population level xi(t); the birth rate function βij(t)xi(t – τij(t))e–γij(t)xi(t–τij(t)) depends on maturation delays τij(t) and the maximum reproduction rate 1 γij (t). A recent study in [10] established the existence and global stability of almost-periodic solutions for Nicholson’s blowflies system (1.1) involving a positive constant M > κ obeying γij(t)M ≤ κ, for all t ∈ R, i ∈ Q, j ∈ I = {1, 2, . Inspired by the above analysis, in this paper, under the weaker assumptions (1.7)–(1.10), we develop a novel approach to demonstrate the global stability of positive asymptotically almost-periodic solutions for system (1.1).
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