Abstract
Bifurcations of the steady homogeneous solution of a simpel reaction-diffusion system, distributed over a one-dimensional discrete lattice, are examined, and the different types of steady spatially inhomogeneous solutions that can appear are indicated. Bifurcations in the infinite-dimensional system are related to branchings (see below) of a two-dimensional area-preserving map, and the result is applied to establish the appearance and stability of wavelength-two solutions. Looking into bifurcations of these wavelength-two solutions, we show that no futher wavelength doubling takes place. The possibility of appearance of spatially chaotic time-invariant structures, and of more complex spatio-temporal structures including temporal intermittency, is briefly speculated upon.
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