Stationary patterns of strongly coupled prey–predator models

By Mingxin Wang. 2004

48 citations recorded by the source corpus.

Abstract We study some elliptic systems arising from 3-component predator–prey models, where cross-diffusions are included in such a way that predator chases the prey and the prey runs away from the predator. We establish the existence and non-existence of non-constant positive solutions. Our results show that the cross-diffusions can create the stationary patterns.

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

View Paper: https://www.semanticscholar.org/paper/eaddebce89a4b3ac1219f6832ed292ac80807f76

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. Zhifu Xie
2. Mingxin Wang
3. Junping Shi

In Modeling and Simulation

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

In Public Health, Environmental and Occupational Health

1. Zhifu Xie
2. Mingxin Wang
3. Rui Peng
4. Yihong Du
5. Peter Y. H. Pang
6. Junping Shi
7. Yang Zhang
8. Meng Zhao

Citations in the corpus

• Cross-diffusion induced Turing instability for a three species food chain model (2012, background): “In [25], the author studied an elliptic system which models the dynamics of a two-preys–one-predator ecosystem and he showed that the cross-diffusions can create the stationary patterns where cross-diffusions are included in such a way that the predator chases the prey and the prey runs away from th”
• 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.”