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

Toshiyuki OGAWA | Zendy; Takashi Okuda | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Toshiyuki OGAWA,

Takashi Okuda

Publication year - 2012

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2012.7.893

Subject(s) - center manifold , hopf bifurcation , reaction–diffusion system , degenerate energy levels , chaotic , instability , bifurcation , neumann boundary condition , mathematical analysis , physics , diffusion , dynamics (music) , equilibrium point , boundary (topology) , stability (learning theory) , classical mechanics , mathematics , mechanics , nonlinear system , quantum mechanics , computer science , artificial intelligence , acoustics , differential equation , machine learning

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research