Dynamics for a type of general reaction–diffusion model

Traveling Wavefronts of a Diffusive Hematopoiesis Model with Time Delay

“…Wang [15] investigated the generalized equation with Neumann boundary condition and obtained the oscillatory behavior of solutions about the positive equilibrium of (1.3). Further, they derived the sufficient and necessary conditions for global attractivity of the zero solution.…”

The study of a fourth-order multistep ADI method applied to nonlinear delay reaction–diffusion equations

“…(1.1) reduces to Mackey-Glass equation [29], which simulates a single-species population with age-structure and diffusion. As f (u(x, t), u(x, t−τ ),…”

“…(1.1), which are referred to [1,6,21,23,29,31]), show that the effect of the delay terms on their dynamic properties is enormous.…”

Global Attractivity of a Diffusive Nicholson's Blowflies Equation with Multiple Delays

“…under Neumann boundary condition and gave the similar sufficient conditions for oscillation of all positive solutions about the positive steady state. Whereafter, many authors studied the various dynamical behaviors for this equation; we refer to Lin and Mei [11], Saker [12], Wang and Li [13], and Yi and Zou [14]. Meanwhile, one can consider a nonlinear equation with several delays because of variability of the generation time; for this purpose, Györi and Ladas [15] and Kulenović and Ladas [6] proposed the following generalized Nicholson's blowflies model:…”

“…, , are all positive constants, Ω ⊂ R is a bounded domain with a smooth boundary Ω, Δ ( , ) = ∑ =1 (( 2 ( , ))/( 2 )), ( / ]) denotes the exterior normal derivative on Ω, and ( , ) is Hölder continuous in with (0, ) ∈ 1 (Ω). Though the global attractivity of the nonnegative equilibria of (2) has been studied by Yang and So [10] and Wang and Li [13,17], they just gave some sufficient conditions. Furthermore, as far as we know, the stability for partial functional differential equations with several delays was investigated by few papers.…”