Bifurcation and pattern formation in a coupled higher autocatalator reaction diffusion system. (English) Zbl 1231.35100
Summary: Spatiotemporal structures arising in two identical cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst, are discussed. The stability of the unique homogeneous steady state is obtained by the linearized theory. A necessary condition for bifurcations in spatially non-uniform solutions in uncoupled and coupled systems is given. Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory. Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35K55 | Nonlinear parabolic equations |
| 35B32 | Bifurcations in context of PDEs |
| 92E20 | Classical flows, reactions, etc. in chemistry |
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