Qualitative behaviour of positive solutions of a predator—prey model: effects of saturation

By Yihong Du, Yuan Lou. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2001

105 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/79360102cb589cc890454eecc52d7230d04f208c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Mingxin Wang
2. Rui Peng
3. Junping Shi
4. Yihong Du
5. Junjie Wei
6. Peter Y. H. Pang
7. Zhigui Lin
8. Yang Zhang

In Modeling and Simulation

1. Rui Peng
2. Mingxin Wang
3. Junping Shi
4. Yihong Du
5. Peter Y. H. Pang
6. Junjie Wei
7. Fengqi Yi
8. Yuan Lou

In Public Health, Environmental and Occupational Health

1. Junping Shi
2. Rui Peng
3. Mingxin Wang
4. Junjie Wei
5. Yihong Du
6. Peter Y. H. Pang
7. Fengqi Yi
8. Jinfeng Wang

Citations in the corpus

• Positive steady states of the Holling–Tanner prey–predator model with diffusion (2005, methodology): “These include the Gierer–Meinhardt model [11, 26], the Sel’kov model [5, 25], the Brusselator model [2], the chemotactic diffusion model [24], the Lotka–Volterra competition model [14,15], the Lotka–Volterra predator–prey model [6, 7 ,12,19,20], as well as models of semiconductors, plasmas, chemical”
• Strategy and stationary pattern in a three-species predator–prey model (2004, methodology): “These include the Gierer–Meinhardt model [14,18,39–41], the Sel’kov model [11,36], the Noyes–Field model for Belousov–Zhabotinskii reaction [31], the chemotactic diffusion model [21,38], the competition model [6,10,22–24], the predator–prey model [7,8,12,13,17,19,20,29,30,37], as well as models of s”
• Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, background): “3 of [5]) gives a complete understanding of the solution of the associated dynamics of (1.”
• Non-constant positive steady states of the Sel'kov model ☆ (2003, methodology): “A variation of the bifurcation technique is through a powerful Leray–Schauder degree theory(incorporated with difficult a priori estimates); see [25–27] for competition models, and [5, 9 ,10,21,37] for predator–preymodels.”
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ (2009, background): “Du and Lou [10] studied a slightly different model and obtained various asymptotic behavior of the steady state solutions when some parameters are large or small.”
• Allee effect and bistability in a spatially heterogeneous predator-prey model (2007, background): “On the other hand, when the environment is homogeneous (a(x) ≡ a), the set of steady state solutions of (1.2) was studied in [ DL3 ] for the large m case (see also [BB, CEL, DL1, DL2] for Dirichlet problems), and for small m, it follows from results in [dMR] that the system has at most one positive ”