Abstract:

The wave equations of the hyperbolic reaction-diffusion equations for the low-concentration Brusselator are developed, and the stability of steady state, especially Turing instability, is studied. The results show that the Turing instability in hyperbolic equations is not confined by the condition that coefficients are not equal(Dx≠Dy). Bifurcation analyses are carried out and the limit cycle is discussed. The numerical studies are also made.

Key words: Brussellator, Hyperbolic(Parabolic) reaction-diffusion equation, Turing instability, Bifureation analysis