We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
We study a generalized Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we employ a novel proof to establish some criteria guaranteeing the permanence of this model. Moreover, we give an example to illustrate our main result.
The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.
We study solutions tending to nonzero constants for the third order differential equation with the damping term in the case when the corresponding second order differential equation is oscillatory.