Abstract
A new set of nonlinear equations for toroidal ion-temperature-gradient-driven ( ITGD) drift-dissipative waves is derived by using Braginskii's transport model of the ion dynamics and the Boltzmann distribution of electrons in the presence of negatively charged dust grains. The temporal behaviour of the nonlinear ITGD mode is found to be governed by three nonlinear equations for the amplitudes, which is a generalization of Lorenz- and Stenflo-type equations admitting chaotic trajectories. The linear stability analysis has been presented and stationary points for our generalized mode coupling equations are also derived.