Non-constant positive steady states of the Sel'kov model ☆

By Mingxin Wang. 2003

133 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/5218676d51c1292aae59e4ccdbaa86ef56f0acd5

How researchers see this paper

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

In Control and Systems Engineering

1. Rui Peng
2. Peter Y. H. Pang
3. Junping Shi
4. Junjie Wei
5. Jinfeng Wang
6. Mingxin Wang
7. D. Naimen

In Modeling and Simulation

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

In Public Health, Environmental and Occupational Health

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

Citations in the corpus

• On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law (2008, unknown): “By the same arguments as in [17, 21, 28], we can assert the following:”
• Non‐Constant Positive Steady States of a Predator‐Prey System with Non‐Monotonic Functional Response and Diffusion (2004, methodology): “A variation of the bifurcation technique is the powerful Leray--Schauder degree approach which involves diLcult a priori estimates; see [27, 28, 29] for its application to competition models and [5, 10, 11, 34, 39] for predator-prey models.”
• Positive steady states of the Holling–Tanner prey–predator model with diffusion (2005, methodology): “d1) = 0, we have the remark similar to remark 5.1 in [ 25 ].”
• 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”
• Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey (2011, unknown): “Without such lower bound, one is not able to use the powerful Leray–Schauder degree theory to prove the existence of nonconstant steady states as in [28,29,37,38,55].”
• Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion (2004, methodology): “These include the Gierer–Meinhardt model [11,18,38,41], the Sel’kov model [7, 35 ], the Gray–Scott model [39], the Ginzburg–Landau equation [29], the Brusselator model [1], the Noyes–Field model for Belousov–Zhabotinskii reaction [32], the chemotactic diffusion model [22,37], the Lotka–Volterra comp”
• Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems (2016, methodology): “To show the existence of non-constant positive solutions, we use Leray–Schauder degree theory (see [24,31,34,45,46]).”
• Qualitative analysis of steady states to the Sel'kov model (2007, methodology): “…of nonconstant positive solutions to (1.1) with respect to the parameter θ is concerned, by use of the argument of topological degree, Wang [20] showed If L m is odd, then there exists a positive constant Θ such that (1.1) admits at least one nonconstant positive solution provided that θ…”
• On pattern formation in the Gray-Scott model (2007, methodology): “by the same argument as in [8] (or [ 9 ]), we can assert the following conclusion: Proposition 3.1.”
• Pattern formation in the Brusselator system (2005, methodology): “For the related works on the patterns of other models, such as the Sel’kov model, the Belousov–Zhabotinski model from chemistry and the models from biology, one may refer to [3,5,10,11,15,19,20,25, 28 ,29], etc.”