Effects of a degeneracy in a diffusive predator–prey model with Holling II functional response

Effects of dispersal for a predator-prey model in a heterogeneous environment

“…Besides, the effect of a protection zone has been studied for predator-prey model with strong Allee effect [2], Leslie predator-prey model [6], ratio-dependent predator-prey model [23], Beddington-DeAngelis predator-prey model [7,21], and Lotka-Volterra competition model [5]. Finally, we point out that a related but different situation for the Holling type II predator-prey model, called a degeneracy, is studied in [4,[12][13][14] and references therein.…”

The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response

“…Lv et al [11] considered a model to describe the harvesting for the phytoplankton and zooplankton based on plausible toxic-phytoplankton-zooplankton systems. Shanbing Li et al [12] studied a spatially heterogeneous predator-prey model where the interaction is governed by…”

A spatially heterogeneous predator-prey model

“…To make sure that indeed P µ (C) is bounded we can argue as follows. The second estimate of(29) shows that µ must be bounded below. The first one provides us with an upper bound for µ,…”

“…is the Laplace operator in R N , and either Γ 1 1 = Γ 2 1 = ∅, i.e., B 1 and B 2 equal the Dirichlet operator on ∂Ω, or Γ 1 0 = Γ 2 0 = ∅, β 1 = β 2 = 0 and ν 1 = ν 2 is the exterior normal vector field; so, B 1 and B 2 equal the Neumann boundary operator. Among the contributions within the first category count those of R. Peng, M. X. Wang and W. Y. Chen [47], M. X. Wang and Q. Wu [49], H. Nie and J. Wu [44], G. Guo and J. Wu [19], [20], J. Zhou and C. Mu [52], J. Zhou and J. P. Shi [54], H. Jiang and L. Wang [24], H. Yuan, J. Wu, Y. Jia and H. Nie [50], S. Li, J. Wu and Y. Dong [29], and X. Feng, Y. Song and X.…”

“…Du and S. B. Hsu [10], W. Ko and K. Ryu [25], [27], Y. Du and J. P. Shi [14], J. Zhou and C. Mu [53], Y. Jia, J. Wu and H. K. Xu [23], S. Li, J. Wu and Y. Dong [29], and X. Zeng, W. Zeng and L. Liu [51]. Another fraction of available literature, like K. Ryu and I. Ahn [48], [26] dealt with Robin boundary conditions.…”