  We present an analytical model describing complex dynamics of a hybrid
nonlinear system consisting of interacting carbon nanotubes (CNT) and a
plasmonic metamaterial. Our model is based on the set of coupled equations,
which incorporates well-established density matrix formalism appropriate for
quantum systems (CNT are described as a two level system) and
harmonic-oscillator approach ideal for modelling sub-wavelength plasmonic and
optical resonators. We show that the saturation nonlinearity of CNT increases
multifold in the resonantly enhanced near field of a metamaterial. In the
framework of our model, we discuss the effect of inhomogeneity of the CNT layer
(band gap value distribution) on the nonlinearity enhancement. It is shown,
that the Purcell effect is indistinguishable from the field enhancement and is
described by the same phenomenological constant.
