Qualitative analysis of steady states to the Sel'kov model

By Rui Peng. 2007

62 citations recorded by the source corpus.

In this work, we are concerned with a reaction–diffusion system well known as the Sel'kov model, which has been used for the study of morphogenesis, population dynamics and autocatalytic oxidation reactions. We derive some further analytic results for the steady states to this model. In particular, we show that no nonconstant positive steady state exists if 0 1 and large θ, where nonconstant positive steady states can occur. Thus, these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants. The a priori estimates are fundamental to our mathematical approaches.

Subfields: Computer Networks and Communications, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/e95959099f1adfb897ae97999481a035b28c586c

How researchers see this paper

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

In Computer Networks and Communications

1. Junping Shi
2. Rui Peng
3. Junjie Wei
4. Jinfeng Wang

In Modeling and Simulation

1. Junping Shi
2. Rui Peng
3. Yuan Lou
4. Mingxin Wang
5. Biao Wang
6. Yihong Du
7. Junjie Wei
8. Xingfu Zou

In Public Health, Environmental and Occupational Health

1. Junping Shi
2. Rui Peng
3. Junjie Wei
4. Yuan Lou
5. Jinfeng Wang
6. Mingxin Wang
7. Biao Wang
8. Xingfu Zou

Citations in the corpus

• Mathematical analysis and numerical simulation of pattern formation under cross-diffusion (2013, unknown): “Several works have been proposed to investigate the existence and uniqueness of weak or global solutions for (1.1) (see [9] [10] [11] [12]) and the behavior of stationary states (see e.g. [13] [14] [15] [16] [17]).”
• Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, background): “Some of these results can be found in [30] or [32].”
• On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law (2008, unknown): “, [20]), but are still stated here for the reader’s convenience.”