The existence and stability of nontrivial steady states for S-K-T competition model with cross diffusion

Wei Ming Ni, Yaping Wu, Qian Xu

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

This paper concerns with the existence and stability properties of non-constant positive steady states in one dimensional space for the following competition system with cross diffusion (Equation presented) by Lyapunov-Schmidt method, we obtain the existence and the detailed structure of a type of small nontrivial positive steady states to the shadow system of (1) as ρ12 → ∞ and when d2 is near a22, which also verifies some related existence results obtained earlier in [11] by a different method. Then, based on the detailed structure of the steady states, we further establish the stability of the small nontrivial positive steady states for the shadow system by spectral analysis. Finally, we prove the existence and stability of the corresponding nontrivial positive steady states for the original cross diffusion system (1) when ρ12 is large enough and d2 is near a 22.

Original languageEnglish (US)
Pages (from-to)5271-5298
Number of pages28
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number12
DOIs
StatePublished - Dec 2014

Keywords

  • Cross diffusion
  • Existence
  • Shadow system
  • Spectral analysis
  • Stability
  • Steady states

Fingerprint Dive into the research topics of 'The existence and stability of nontrivial steady states for S-K-T competition model with cross diffusion'. Together they form a unique fingerprint.

Cite this