Locus Nodal

The locus of these Hopf bifurcation points is also shown in Fig. 4.3 and can be seen to be another closed loop emanating from the origin. It lies in the region between the loci for changes between nodal and focal character, so the condition tr(J) separates stable focus from unstable focus. The curve has a maximum at... 

We may also note, for the special case / = 1, that the locus described by eqns (10.58) and (10.59) is exactly that corresponding to the boundary between unstable focus and unstable node for the well-stirred system. This seems to be a general equivalence between the existence of unstable nodal solutions in the well-stirred system and the possibility of diffusion-driven pattern formation in the absence of stirring. We have seen in chapter 5 that unstable nodes are not found in the present model if the full Arrhenius rate law is used and the activation energy is low, i.e. iff <4 RTa. In that case we would also not expect spatial instability. 

A nodal plane or surface is the locus of all points at which a wave-function has zero amplitude as a result of its changing sign on passing from one side of the surface to the other the probability of finding an electron on such a surface is zero. o-Bonds and o-orbitaJs are defined as those having no nodal surface which contains the bond axis such bonds and orbitals will be symmetric about the bond axis. In this section we consider which AOs of a central atom A (which is bonded to a set of other atoms) can be combined to form a hybrid orbital which is symmetric about the bond axis and therefore capable of cr-bonding. 

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