Oscillatory dynamics in a reaction-diffusion system in the presence of 0:1:2 resonance

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Oscillatory dynamics in a reaction-diffusion system with spatially nonlocal effect under Neumann boundary conditions is studied. The system provides triply degenerate points for two spatially non-uniform modes and uniform one (zero mode). We focus our attention on the 0:1:2-mode interaction in the reaction-diffusion system. Using a normal form on the center manifold, we seek the equilibria and study the stability of them. Moreover, Hopf bifurcation phenomena is studied for each equilibrium which has a Hopf instability point. The numerical results to the chaotic dynamics are also shown.

Original languageEnglish
Pages (from-to)893-926
Number of pages34
JournalNetworks and Heterogeneous Media
Volume7
Issue number4
DOIs
Publication statusPublished - 2012

Keywords

  • 0:1:2 resonance
  • Chaotic dynamics
  • Hopf bifurcation
  • Normal form
  • Triply degenerate point

Fingerprint Dive into the research topics of 'Oscillatory dynamics in a reaction-diffusion system in the presence of 0:1:2 resonance'. Together they form a unique fingerprint.

Cite this