Criteria of global attraction in systems of delay differential equations with mixed monotonicity

Permanence for Nonautonomous Differential Systems with Delays in the Linear and Nonlinear Terms

“…As illustrated by Berezansky and Braveman [15], though small delays are in general harmless, the presence of two or more delays in the same nonlinear function may change drastically the global properties of the solutions. The permanence and stability of DDEs with nonlinearities of mixed monotonicity have been analyzed in [1,8,15,16,32]. As far as the author knows, only the case of discrete delays has been dealt with.…”

“…See also in [Section 4] of [23], for a two species competition model. Meanwhile, a general nonautonomous n-dimensional version of the model in (32), which can be interpreted as a structured population model, was considered and studied in [5,9]:…”

Permanence for nonautonomous differential systems with delays in the linear and nonlinear terms

“…As as illustrated by Berezansky and Braveman [3], though small delays are in general harmless, the presence of two or more delays in the same nonlinear function may change drastically the global properties of the solutions. The permanence and stability of DDEs with nonlinearities of mixed monotonicity have been analyzed in [2,3,7,13,15]. As far as the author knows, only the case of discrete delays has been dealt with.…”

Stability and periodic solutions for Nicholson equations with mixed monotone terms

“…For some selected works on autonomous scalar models, see [3,19,27,28,40] as well as additional references in Section 2. Among many other real world applications, we stress that generalized and modified versions of (1.1) include a neoclassic growth model used in economics [20], periodic equations [3,5,6,13,22] and systems [12] to account for periodic environments (as treated in Section 4), a diffusive Nicholson's equation derived as a suitable model for an age structured single species population [16,38,39], ndimensional Nicholson's systems with patch structured used in population dynamics [10,15,23,24,41] or as compartmental leukemia and marine models [4], etc.…”