Spatially inhomogeneous structures in a onehyphen;dimensional array of Brussellators

摘要

Considering a onehyphen;dimensional array of diffusively coupled Brussellators, we examine the bifurcations of the steady homogeneous solution to steady but spatially inhomogeneous structures. Several important aspects of such bifurcations are related to branching (see below) of the fixed point of a fourhyphen;dimensional conservative map. In addition to the usual period doubling (lsquo;lsquo;wavelength doublingrsquo;rsquo; in our terminology) observed in case of twohyphen;dimensional maps, the fourhyphen;dimensional map is seen to exhibit a new type of branching, namely, giving rise to an invariant curve in phase space. In case of subthreshold branching of either type, the steady homogeneous solution bifurcates to either a lsquo;lsquo;wavelengthhyphen;tworsquo;rsquo; or a quasiperiodic solution. In case of superthreshold branching, on the other hand, bifurcations involving more complicated spatial and temporal behavior are possible. Other relevant questions are dealt with.