  We studied complex spectra of spin-two boson systems represented by
E$\otimes$e and E$\otimes (b_1+b_2)$ Jahn-Teller models. For E$\otimes$e, at
particular rotation quantum numbers we found a coexistence of up to three
regions of the spectra, (i) the dimerized region of long-range ordered
(extended) pairs of oscillating levels, (ii) the short-range ordered
(localized) "kink lattice" of avoiding levels, and (iii) the intermediate
region of kink nucleation with variable range of ordering. This structure
appears above certain critical line as a function of interaction strength. The
level clustering and level avoiding generic patterns reflect themselves in
several intermittent regions between up-to three branches of spectral
entropies. Linear scaling behavior of the widths of curvature probability
distributions provides the conventionally adopted indication for the presence
of quantum chaos. The mapping onto classical integrable Calogero-Moser gas
provided useful insight into the complex level dynamics, including the soliton
collisions representing the level avoidings and, in a range of model
parameters, a novel view on the notion of quantum chaos formulated in terms of
quantum numbers via the logistic equation. We found that apart from two
limiting cases of $E\otimes(b_1+b_2)$ model ($E\otimes e$ and Holstein model)
the distribution of nearest neighbor spacings of this model is rather stable as
to the change of parameters and different from Wigner one. This limiting
distribution assumably shows scaling $\sim\sqrt{S}$ at small $S$ and resembles
the semi-Poisson law $P(S)= 4S \exp (-2 S)$ at $S\geq 1$. The latter is
believed to be universal and characteristic, e.g. at the transition between
metal and insulator phases.
